diff --git a/src/Bridges/Constraint/bridges/IntegerToZeroOneBridge.jl b/src/Bridges/Constraint/bridges/IntegerToZeroOneBridge.jl
index 136d64905e..911b28f62a 100644
--- a/src/Bridges/Constraint/bridges/IntegerToZeroOneBridge.jl
+++ b/src/Bridges/Constraint/bridges/IntegerToZeroOneBridge.jl
@@ -152,7 +152,8 @@ function MOI.Bridges.final_touch(
     bridge::IntegerToZeroOneBridge{T},
     model::MOI.ModelLike,
 ) where {T}
-    ret = MOI.Utilities.get_bounds(model, T, bridge.x)
+    # Type annotation needed for JET
+    ret = MOI.Utilities.get_bounds(model, T, bridge.x)::Tuple{T,T}
     if ret === bridge.last_bounds
         return nothing  # final_touch already called
     elseif ret[1] == typemin(T) || ret[2] == typemax(T)
diff --git a/src/Bridges/Constraint/bridges/SplitIntervalBridge.jl b/src/Bridges/Constraint/bridges/SplitIntervalBridge.jl
index ab720e9f46..a0c789f932 100644
--- a/src/Bridges/Constraint/bridges/SplitIntervalBridge.jl
+++ b/src/Bridges/Constraint/bridges/SplitIntervalBridge.jl
@@ -325,17 +325,15 @@ function MOI.get(
         upper_stat = MOI.get(model, attr, bridge.upper)
         if upper_stat == MOI.NONBASIC
             return MOI.NONBASIC_AT_UPPER
+        elseif bridge.lower === nothing
+            return upper_stat
         end
-    end
-    if bridge.lower === nothing
-        if bridge.upper === nothing
-            # The only case where the interval `[-∞, ∞]` is allowed is for
-            # `VariableIndex` constraints but `ConstraintBasisStatus` is not
-            # defined for `VariableIndex` constraints.
-            msg = "Cannot get `$attr` for a constraint in the interval `[-Inf, Inf]`."
-            throw(MOI.GetAttributeNotAllowed(attr, msg))
-        end
-        return upper_stat
+    elseif bridge.lower === nothing
+        # The only case where the interval `[-∞, ∞]` is allowed is for
+        # `VariableIndex` constraints but `ConstraintBasisStatus` is not
+        # defined for `VariableIndex` constraints.
+        msg = "Cannot get `$attr` for a constraint in the interval `[-Inf, Inf]`."
+        throw(MOI.GetAttributeNotAllowed(attr, msg))
     end
     lower_stat = MOI.get(model, attr, bridge.lower)
     if lower_stat == MOI.NONBASIC
diff --git a/src/Bridges/Constraint/single_bridge_optimizer.jl b/src/Bridges/Constraint/single_bridge_optimizer.jl
index 496447f25e..a70d118cb3 100644
--- a/src/Bridges/Constraint/single_bridge_optimizer.jl
+++ b/src/Bridges/Constraint/single_bridge_optimizer.jl
@@ -48,15 +48,15 @@ mutable struct SingleBridgeOptimizer{BT<:AbstractBridge,OT<:MOI.ModelLike} <:
     map::Map # index of bridged constraint -> constraint bridge
     con_to_name::Dict{MOI.ConstraintIndex,String}
     name_to_con::Union{Dict{String,MOI.ConstraintIndex},Nothing}
-end
 
-function SingleBridgeOptimizer{BT}(model::OT) where {BT,OT<:MOI.ModelLike}
-    return SingleBridgeOptimizer{BT,OT}(
-        model,
-        Map(),
-        Dict{MOI.ConstraintIndex,String}(),
-        nothing,
-    )
+    function SingleBridgeOptimizer{BT}(model::OT) where {BT,OT<:MOI.ModelLike}
+        return new{BT,OT}(
+            model,
+            Map(),
+            Dict{MOI.ConstraintIndex,String}(),
+            nothing,
+        )
+    end
 end
 
 bridges(::MOI.Bridges.AbstractBridgeOptimizer) = EmptyMap()
diff --git a/src/Bridges/Objective/single_bridge_optimizer.jl b/src/Bridges/Objective/single_bridge_optimizer.jl
index bd6be6bde2..d0eac538e2 100644
--- a/src/Bridges/Objective/single_bridge_optimizer.jl
+++ b/src/Bridges/Objective/single_bridge_optimizer.jl
@@ -41,10 +41,10 @@ mutable struct SingleBridgeOptimizer{BT<:AbstractBridge,OT<:MOI.ModelLike} <:
                MOI.Bridges.AbstractBridgeOptimizer
     model::OT
     map::Map # `MOI.ObjectiveFunction` -> objective bridge
-end
 
-function SingleBridgeOptimizer{BT}(model::OT) where {BT,OT<:MOI.ModelLike}
-    return SingleBridgeOptimizer{BT,OT}(model, Map())
+    function SingleBridgeOptimizer{BT}(model::OT) where {BT,OT<:MOI.ModelLike}
+        return new{BT,OT}(model, Map())
+    end
 end
 
 bridges(::MOI.Bridges.AbstractBridgeOptimizer) = EmptyMap()
diff --git a/src/Bridges/Variable/single_bridge_optimizer.jl b/src/Bridges/Variable/single_bridge_optimizer.jl
index 3b7ca9a022..5d466cb609 100644
--- a/src/Bridges/Variable/single_bridge_optimizer.jl
+++ b/src/Bridges/Variable/single_bridge_optimizer.jl
@@ -50,17 +50,17 @@ mutable struct SingleBridgeOptimizer{BT<:AbstractBridge,OT<:MOI.ModelLike} <:
     name_to_var::Union{Dict{String,MOI.VariableIndex},Nothing}
     con_to_name::Dict{MOI.ConstraintIndex,String}
     name_to_con::Union{Dict{String,MOI.ConstraintIndex},Nothing}
-end
 
-function SingleBridgeOptimizer{BT}(model::OT) where {BT,OT<:MOI.ModelLike}
-    return SingleBridgeOptimizer{BT,OT}(
-        model,
-        Map(),
-        Dict{MOI.VariableIndex,String}(),
-        nothing,
-        Dict{MOI.ConstraintIndex,String}(),
-        nothing,
-    )
+    function SingleBridgeOptimizer{BT}(model::OT) where {BT,OT<:MOI.ModelLike}
+        return new{BT,OT}(
+            model,
+            Map(),
+            Dict{MOI.VariableIndex,String}(),
+            nothing,
+            Dict{MOI.ConstraintIndex,String}(),
+            nothing,
+        )
+    end
 end
 
 bridges(::MOI.Bridges.AbstractBridgeOptimizer) = EmptyMap()
diff --git a/src/Bridges/bridge_optimizer.jl b/src/Bridges/bridge_optimizer.jl
index 9851d1ace9..a13ab5093d 100644
--- a/src/Bridges/bridge_optimizer.jl
+++ b/src/Bridges/bridge_optimizer.jl
@@ -2389,7 +2389,10 @@ end
 Substitute any bridged [`MOI.VariableIndex`](@ref) in `value` by an equivalent
 expression in terms of variables of `b.model`.
 """
-function bridged_function(bridge::AbstractBridgeOptimizer, value)
+function bridged_function(
+    bridge::AbstractBridgeOptimizer,
+    value::V,
+)::V where {V}
     if !Variable.has_bridges(Variable.bridges(bridge))
         # Shortcut, this allows performance to be unaltered when no variable
         # bridges are used.
@@ -2398,10 +2401,9 @@ function bridged_function(bridge::AbstractBridgeOptimizer, value)
     # We assume that the type of `value` is not altered. This restricts
     # variable bridges to only return `ScalarAffineFunction` but otherwise,
     # the performance would be bad.
-    return MOI.Utilities.substitute_variables(
-        vi -> bridged_variable_function(bridge, vi),
-        value,
-    )::typeof(value)
+    return MOI.Utilities.substitute_variables(value) do vi
+        return bridged_variable_function(bridge, vi)
+    end
 end
 
 function bridged_function(b::AbstractBridgeOptimizer, func::MOI.VariableIndex)
diff --git a/src/FileFormats/LP/read.jl b/src/FileFormats/LP/read.jl
index 48a0da2893..2aac656a7c 100644
--- a/src/FileFormats/LP/read.jl
+++ b/src/FileFormats/LP/read.jl
@@ -511,6 +511,11 @@ end
 
 _is_number(c::Char) = isdigit(c) || c in ('.', 'e', 'E', '+', '-')
 
+function _is_negative_digit(state, c)
+    # The type annotation is needed for JET.
+    return c == '-' && isdigit(peek(state, Char)::Char)
+end
+
 function _peek_inner(state::_LexerState)
     while (c = peek(state, Char)) !== nothing
         pos = position(state.io)
@@ -523,7 +528,7 @@ function _peek_inner(state::_LexerState)
             while (c = peek(state, Char)) !== nothing && c != '\n'
                 _ = read(state, Char)
             end
-        elseif isdigit(c) || (c == '-' && isdigit(peek(state, Char))) # Number
+        elseif isdigit(c) || _is_negative_digit(state, c) # Number
             buf = IOBuffer()
             while (c = peek(state, Char)) !== nothing && _is_number(c)
                 write(buf, c)
@@ -826,7 +831,8 @@ function _parse_term(
         # <quadratic-expression>
         return _parse_quadratic_expression(state, cache, prefix)
     end
-    token = peek(state, _Token)
+    # The type annotation is needed for JET.
+    token = peek(state, _Token)::_Token
     return _throw_parse_error(
         state,
         token,
@@ -1050,7 +1056,8 @@ function _parse_constraint_sos(
     f, w = MOI.VectorOfVariables(MOI.VariableIndex[]), T[]
     while true
         if _next_token_is(state, _TOKEN_NEWLINE)
-            t = peek(state, _Token)
+            # The type annotation is needed for JET.
+            t = peek(state, _Token)::_Token
             _throw_parse_error(
                 state,
                 t,
@@ -1096,7 +1103,8 @@ function _parse_constraint_indicator(
     end
     _ = read(state, _Token, _TOKEN_IMPLIES)
     f = _parse_expression(state, cache)
-    set = _parse_set_suffix(state, cache)
+    # The type annotation is needed for JET.
+    set = _parse_set_suffix(state, cache)::MOI.AbstractScalarSet
     return MOI.add_constraint(
         cache.model,
         MOI.Utilities.operate(vcat, T, z, f),
@@ -1117,7 +1125,8 @@ function _parse_constraint(state::_LexerState, cache::_ReadCache)
         _parse_constraint_indicator(state, cache)
     else
         f = _parse_expression(state, cache)
-        set = _parse_set_suffix(state, cache)
+        # The type annotation is needed for JET.
+        set = _parse_set_suffix(state, cache)::MOI.AbstractScalarSet
         MOI.add_constraint(cache.model, f, set)
     end
     if name !== nothing
diff --git a/src/FileFormats/MPS/read.jl b/src/FileFormats/MPS/read.jl
index 29d5162d9e..8fe37111e8 100644
--- a/src/FileFormats/MPS/read.jl
+++ b/src/FileFormats/MPS/read.jl
@@ -432,7 +432,8 @@ function _add_indicator_constraint(
         scalar = MOI.ScalarAffineTerm(coef, variable_map[data.col_to_name[i]])
         push!(terms, MOI.VectorAffineTerm(2, scalar))
     end
-    f = MOI.VectorAffineFunction(terms, zeros(T, 2))
+    # The type annotation is needed for JET.
+    f = MOI.VectorAffineFunction(terms, zeros(T, 2)::Vector{T})
     c = MOI.add_constraint(model, f, MOI.Indicator{activate}(set))
     MOI.set(model, MOI.ConstraintName(), c, c_name)
     return
diff --git a/src/FileFormats/NL/read.jl b/src/FileFormats/NL/read.jl
index 267edea6e3..28e718a4ff 100644
--- a/src/FileFormats/NL/read.jl
+++ b/src/FileFormats/NL/read.jl
@@ -271,13 +271,15 @@ _try_scalar_affine_function(x::MOI.VariableIndex) = x
 function _try_scalar_affine_function(expr::Expr)
     if expr.args[1] == :+
         args = _try_scalar_affine_function.(expr.args[2:end])
-        if any(isnothing, args)
+        # The type annotation is needed for JET.
+        if any(isnothing, args)::Bool
             return nothing
         end
         return MOI.Utilities.operate(+, Float64, args...)
     elseif expr.args[1] == :*
         args = _try_scalar_affine_function.(expr.args[2:end])
-        if any(isnothing, args)
+        # The type annotation is needed for JET.
+        if any(isnothing, args)::Bool
             return nothing
         end
         n_affine_terms = 0
diff --git a/src/Nonlinear/SymbolicAD/SymbolicAD.jl b/src/Nonlinear/SymbolicAD/SymbolicAD.jl
index b1c4c8573e..9285faa84b 100644
--- a/src/Nonlinear/SymbolicAD/SymbolicAD.jl
+++ b/src/Nonlinear/SymbolicAD/SymbolicAD.jl
@@ -1333,7 +1333,12 @@ function Evaluator(
     constraint_index_by_hash = Dict{UInt64,Vector{Int}}()
     jac_offset, hess_offset = 0, 0
     if model.objective !== nothing
-        o_sym = _to_symbolic_form(model, model.objective, variable_to_column)
+        o_sym = _to_symbolic_form(
+            model,
+            # The type annotation is needed for JET.
+            model.objective::MOI.Nonlinear.Expression,
+            variable_to_column,
+        )
         x, ∇f, H, ∇²f = gradient_and_hessian(x -> x.value > 0, o_sym.f)
         dag = _DAG(model.operators, Any[o_sym.f; ∇f; ∇²f])
         hash_to_dag[o_sym.hash] = dag
diff --git a/src/Test/test_conic.jl b/src/Test/test_conic.jl
index c353ff0a29..3d69c2abbf 100644
--- a/src/Test/test_conic.jl
+++ b/src/Test/test_conic.jl
@@ -2175,6 +2175,8 @@ function _test_conic_RotatedSecondOrderCone_helper(
             MOI.RotatedSecondOrderCone,
         )
     end
+    # These variables are needed for JET.
+    vc1, vc2 = nothing, nothing
     if abvars
         abx, rsoc =
             MOI.add_constrained_variables(model, MOI.RotatedSecondOrderCone(4))
@@ -5938,6 +5940,8 @@ function _test_det_cone_helper_ellipsoid(
     @test MOI.get(model, MOI.NumberOfVariables()) == 1
     Q = MOI.add_variables(model, square ? 4 : 3)
     @test MOI.get(model, MOI.NumberOfVariables()) == (square ? 5 : 4)
+    # These variables are needed for JET.
+    u, vc = nothing, nothing
     if use_logdet
         u = MOI.add_variable(model)
         vc = MOI.add_constraint(model, u, MOI.EqualTo(T(1)))
diff --git a/src/Utilities/cachingoptimizer.jl b/src/Utilities/cachingoptimizer.jl
index 0a37eb4fd6..f3392bbf07 100644
--- a/src/Utilities/cachingoptimizer.jl
+++ b/src/Utilities/cachingoptimizer.jl
@@ -382,48 +382,45 @@ function MOI.optimize!(m::CachingOptimizer)
 end
 
 function MOI.add_variable(m::CachingOptimizer)
-    if m.state == ATTACHED_OPTIMIZER
-        if m.mode == AUTOMATIC
-            try
-                vindex_optimizer =
-                    MOI.add_variable(m.optimizer)::MOI.VariableIndex
-            catch err
-                _rethrow_if_not_NotAllowedError(err)
-                reset_optimizer(m)
-            end
-        else
-            vindex_optimizer = MOI.add_variable(m.optimizer)::MOI.VariableIndex
+    if m.state != ATTACHED_OPTIMIZER
+        return MOI.add_variable(m.model_cache)
+    end
+    vindex_optimizer = if m.mode == AUTOMATIC
+        try
+            MOI.add_variable(m.optimizer)::MOI.VariableIndex
+        catch err
+            _rethrow_if_not_NotAllowedError(err)
+            reset_optimizer(m)
+            return MOI.add_variable(m)
         end
+    else
+        MOI.add_variable(m.optimizer)::MOI.VariableIndex
     end
     vindex = MOI.add_variable(m.model_cache)
-    if m.state == ATTACHED_OPTIMIZER
-        m.model_to_optimizer_map[vindex] = vindex_optimizer
-        m.optimizer_to_model_map[vindex_optimizer] = vindex
-    end
+    m.model_to_optimizer_map[vindex] = vindex_optimizer
+    m.optimizer_to_model_map[vindex_optimizer] = vindex
     return vindex
 end
 
 function MOI.add_variables(m::CachingOptimizer, n)
-    if m.state == ATTACHED_OPTIMIZER
-        if m.mode == AUTOMATIC
-            try
-                vindices_optimizer =
-                    MOI.add_variables(m.optimizer, n)::Vector{MOI.VariableIndex}
-            catch err
-                _rethrow_if_not_NotAllowedError(err)
-                reset_optimizer(m)
-            end
-        else
-            vindices_optimizer =
-                MOI.add_variables(m.optimizer, n)::Vector{MOI.VariableIndex}
+    if m.state != ATTACHED_OPTIMIZER
+        return MOI.add_variables(m.model_cache, n)
+    end
+    vindices_optimizer = if m.mode == AUTOMATIC
+        try
+            MOI.add_variables(m.optimizer, n)::Vector{MOI.VariableIndex}
+        catch err
+            _rethrow_if_not_NotAllowedError(err)
+            reset_optimizer(m)
+            return MOI.add_variables(m, n)
         end
+    else
+        MOI.add_variables(m.optimizer, n)::Vector{MOI.VariableIndex}
     end
     vindices = MOI.add_variables(m.model_cache, n)
-    if m.state == ATTACHED_OPTIMIZER
-        for (vindex, vindex_optimizer) in zip(vindices, vindices_optimizer)
-            m.model_to_optimizer_map[vindex] = vindex_optimizer
-            m.optimizer_to_model_map[vindex_optimizer] = vindex
-        end
+    for (vindex, vindex_optimizer) in zip(vindices, vindices_optimizer)
+        m.model_to_optimizer_map[vindex] = vindex_optimizer
+        m.optimizer_to_model_map[vindex_optimizer] = vindex
     end
     return vindices
 end
@@ -442,38 +439,26 @@ function MOI.add_constrained_variable(
     m::CachingOptimizer,
     set::S,
 ) where {S<:MOI.AbstractScalarSet}
-    if m.state == ATTACHED_OPTIMIZER
-        if m.mode == AUTOMATIC
-            try
-                vindex_optimizer, cindex_optimizer =
-                    MOI.add_constrained_variable(
-                        m.optimizer,
-                        set,
-                    )::Tuple{
-                        MOI.VariableIndex,
-                        MOI.ConstraintIndex{MOI.VariableIndex,S},
-                    }
-            catch err
-                _rethrow_if_not_NotAllowedError(err)
-                reset_optimizer(m)
-            end
-        else
-            vindex_optimizer, cindex_optimizer = MOI.add_constrained_variable(
-                m.optimizer,
-                set,
-            )::Tuple{
-                MOI.VariableIndex,
-                MOI.ConstraintIndex{MOI.VariableIndex,S},
-            }
+    if m.state != ATTACHED_OPTIMIZER
+        return MOI.add_constrained_variable(m.model_cache, set)
+    end
+    R = Tuple{MOI.VariableIndex,MOI.ConstraintIndex{MOI.VariableIndex,S}}
+    vindex_optimizer, cindex_optimizer = if m.mode == AUTOMATIC
+        try
+            MOI.add_constrained_variable(m.optimizer, set)::R
+        catch err
+            _rethrow_if_not_NotAllowedError(err)
+            reset_optimizer(m)
+            return MOI.add_constrained_variable(m, set)
         end
+    else
+        MOI.add_constrained_variable(m.optimizer, set)::R
     end
     vindex, cindex = MOI.add_constrained_variable(m.model_cache, set)
-    if m.state == ATTACHED_OPTIMIZER
-        m.model_to_optimizer_map[vindex] = vindex_optimizer
-        m.optimizer_to_model_map[vindex_optimizer] = vindex
-        m.model_to_optimizer_map[cindex] = cindex_optimizer
-        m.optimizer_to_model_map[cindex_optimizer] = cindex
-    end
+    m.model_to_optimizer_map[vindex] = vindex_optimizer
+    m.optimizer_to_model_map[vindex_optimizer] = vindex
+    m.model_to_optimizer_map[cindex] = cindex_optimizer
+    m.optimizer_to_model_map[cindex_optimizer] = cindex
     return vindex, cindex
 end
 
@@ -506,41 +491,39 @@ function MOI.add_constrained_variables(
     m::CachingOptimizer,
     set::S,
 ) where {S<:MOI.AbstractVectorSet}
-    if m.state == ATTACHED_OPTIMIZER
-        if m.mode == AUTOMATIC
-            try
-                vindices_optimizer, cindex_optimizer =
-                    MOI.add_constrained_variables(
-                        m.optimizer,
-                        set,
-                    )::Tuple{
-                        Vector{MOI.VariableIndex},
-                        MOI.ConstraintIndex{MOI.VectorOfVariables,S},
-                    }
-            catch err
-                _rethrow_if_not_NotAllowedError(err)
-                reset_optimizer(m)
-            end
-        else
-            vindices_optimizer, cindex_optimizer =
-                MOI.add_constrained_variables(
-                    m.optimizer,
-                    set,
-                )::Tuple{
-                    Vector{MOI.VariableIndex},
-                    MOI.ConstraintIndex{MOI.VectorOfVariables,S},
-                }
+    if m.state != ATTACHED_OPTIMIZER
+        return MOI.add_constrained_variables(m.model_cache, set)
+    end
+    vindices_optimizer, cindex_optimizer = if m.mode == AUTOMATIC
+        try
+            MOI.add_constrained_variables(
+                m.optimizer,
+                set,
+            )::Tuple{
+                Vector{MOI.VariableIndex},
+                MOI.ConstraintIndex{MOI.VectorOfVariables,S},
+            }
+        catch err
+            _rethrow_if_not_NotAllowedError(err)
+            reset_optimizer(m)
+            return MOI.add_constrained_variables(m, set)
         end
+    else
+        MOI.add_constrained_variables(
+            m.optimizer,
+            set,
+        )::Tuple{
+            Vector{MOI.VariableIndex},
+            MOI.ConstraintIndex{MOI.VectorOfVariables,S},
+        }
     end
     vindices, cindex = MOI.add_constrained_variables(m.model_cache, set)
-    if m.state == ATTACHED_OPTIMIZER
-        for (vindex, vindex_optimizer) in zip(vindices, vindices_optimizer)
-            m.model_to_optimizer_map[vindex] = vindex_optimizer
-            m.optimizer_to_model_map[vindex_optimizer] = vindex
-        end
-        m.model_to_optimizer_map[cindex] = cindex_optimizer
-        m.optimizer_to_model_map[cindex_optimizer] = cindex
+    for (vindex, vindex_optimizer) in zip(vindices, vindices_optimizer)
+        m.model_to_optimizer_map[vindex] = vindex_optimizer
+        m.optimizer_to_model_map[vindex_optimizer] = vindex
     end
+    m.model_to_optimizer_map[cindex] = cindex_optimizer
+    m.optimizer_to_model_map[cindex_optimizer] = cindex
     return vindices, cindex
 end
 
@@ -560,34 +543,34 @@ function MOI.add_constraint(
     func::F,
     set::S,
 ) where {F<:MOI.AbstractFunction,S<:MOI.AbstractSet}
-    if m.state == ATTACHED_OPTIMIZER
-        if m.mode == AUTOMATIC
-            try
-                cindex_optimizer = MOI.add_constraint(
-                    m.optimizer,
-                    map_indices(m.model_to_optimizer_map, func),
-                    set,
-                )::MOI.ConstraintIndex{F,S}
-            catch err
-                _rethrow_if_not_NotAllowedError(err)
-                # It could be MOI.AddConstraintNotAllowed{F', S'} with F' != F
-                # or S' != S if, for example, the `F`-in-`S` constraint is bridged
-                # to other constraints in `m.optimizer`
-                reset_optimizer(m)
-            end
-        else
-            cindex_optimizer = MOI.add_constraint(
+    if m.state != ATTACHED_OPTIMIZER
+        return MOI.add_constraint(m.model_cache, func, set)
+    end
+    cindex_optimizer = if m.mode == AUTOMATIC
+        try
+            MOI.add_constraint(
                 m.optimizer,
                 map_indices(m.model_to_optimizer_map, func),
                 set,
             )::MOI.ConstraintIndex{F,S}
+        catch err
+            _rethrow_if_not_NotAllowedError(err)
+            # It could be MOI.AddConstraintNotAllowed{F', S'} with F' != F
+            # or S' != S if, for example, the `F`-in-`S` constraint is bridged
+            # to other constraints in `m.optimizer`
+            reset_optimizer(m)
+            return MOI.add_constraint(m, func, set)
         end
+    else
+        MOI.add_constraint(
+            m.optimizer,
+            map_indices(m.model_to_optimizer_map, func),
+            set,
+        )::MOI.ConstraintIndex{F,S}
     end
     cindex = MOI.add_constraint(m.model_cache, func, set)
-    if m.state == ATTACHED_OPTIMIZER
-        m.model_to_optimizer_map[cindex] = cindex_optimizer
-        m.optimizer_to_model_map[cindex_optimizer] = cindex
-    end
+    m.model_to_optimizer_map[cindex] = cindex_optimizer
+    m.optimizer_to_model_map[cindex_optimizer] = cindex
     return cindex
 end
 
diff --git a/src/Utilities/distance_to_set.jl b/src/Utilities/distance_to_set.jl
index ab485cc749..44dcdb85de 100644
--- a/src/Utilities/distance_to_set.jl
+++ b/src/Utilities/distance_to_set.jl
@@ -504,9 +504,13 @@ function _reshape(x::AbstractVector, set::MOI.PositiveSemidefiniteConeSquare)
     return reshape(x, (n, n))
 end
 
-function _reshape(x::AbstractVector, set::MOI.PositiveSemidefiniteConeTriangle)
+function _reshape(
+    x::AbstractVector{T},
+    set::MOI.PositiveSemidefiniteConeTriangle,
+) where {T}
     n = MOI.side_dimension(set)
-    X = zeros(eltype(x), n, n)
+    # The type annotation is needed for JET.
+    X = zeros(T, n, n)::Matrix{T}
     k = 1
     for i in 1:n
         for j in 1:i
diff --git a/src/Utilities/functions.jl b/src/Utilities/functions.jl
index 5826319ec4..e88ae35416 100644
--- a/src/Utilities/functions.jl
+++ b/src/Utilities/functions.jl
@@ -932,12 +932,14 @@ Sums the coefficients of `t1` and `t2` and returns an output
 `variable` of `t1` as the `output_index` and `variable` of the output term
 without checking that they are equal to those of `t2`.
 """
-function unsafe_add(
-    t1::T,
-    t2::T,
-) where {T<:Union{MOI.VectorAffineTerm,MOI.VectorQuadraticTerm}}
+function unsafe_add(t1::MOI.VectorAffineTerm, t2::MOI.VectorAffineTerm)
     scalar_term = unsafe_add(t1.scalar_term, t2.scalar_term)
-    return T(t1.output_index, scalar_term)
+    return MOI.VectorAffineTerm(t1.output_index, scalar_term)
+end
+
+function unsafe_add(t1::MOI.VectorQuadraticTerm, t2::MOI.VectorQuadraticTerm)
+    scalar_term = unsafe_add(t1.scalar_term, t2.scalar_term)
+    return MOI.VectorQuadraticTerm(t1.output_index, scalar_term)
 end
 
 # Generic fallback for items inside NonlinearFunctions like numbers.
diff --git a/src/Utilities/lazy_iterators.jl b/src/Utilities/lazy_iterators.jl
index 1075fefa04..71c100ab05 100644
--- a/src/Utilities/lazy_iterators.jl
+++ b/src/Utilities/lazy_iterators.jl
@@ -31,10 +31,10 @@ depending on the type of `data`.
 struct LazyMap{T,VT,F}
     f::F
     data::VT
-end
 
-function LazyMap{T}(f, data) where {T}
-    return LazyMap{T,typeof(data),typeof(f)}(f, data)
+    function LazyMap{T}(f, data) where {T}
+        return new{T,typeof(data),typeof(f)}(f, data)
+    end
 end
 
 """
@@ -62,10 +62,10 @@ depending on the type of `data`.
 struct VectorLazyMap{T,VT<:AbstractVector,F} <: AbstractVector{T}
     f::F
     data::VT
-end
 
-function VectorLazyMap{T}(f, data) where {T}
-    return VectorLazyMap{T,typeof(data),typeof(f)}(f, data)
+    function VectorLazyMap{T}(f, data) where {T}
+        return new{T,typeof(data),typeof(f)}(f, data)
+    end
 end
 
 function lazy_map(::Type{T}, f, data::AbstractVector) where {T}
diff --git a/src/Utilities/model.jl b/src/Utilities/model.jl
index 93d34e9dc1..fe06b53763 100644
--- a/src/Utilities/model.jl
+++ b/src/Utilities/model.jl
@@ -295,7 +295,9 @@ function MOI.get(model::AbstractModel, ::Type{MOI.VariableIndex}, name::String)
     if model.name_to_var === nothing
         model.name_to_var = build_name_to_var_map(model.var_to_name)
     end
-    result = get(model.name_to_var, name, nothing)
+    # The type annotation is needed for JET.
+    result =
+        get(model.name_to_var::Dict{String,MOI.VariableIndex}, name, nothing)
     throw_if_multiple_with_name(result, name)
     return result
 end
diff --git a/src/Utilities/set_dot.jl b/src/Utilities/set_dot.jl
index a3f7ade562..5abbdc7641 100644
--- a/src/Utilities/set_dot.jl
+++ b/src/Utilities/set_dot.jl
@@ -292,10 +292,10 @@ julia> MOI.Utilities.operate(*, Float64, Diagonal(a), ones(3))
 """
 struct SetDotScalingVector{T,S<:MOI.AbstractSet} <: AbstractVector{T}
     set::S
-end
 
-function SetDotScalingVector{T}(s::MOI.AbstractSet) where {T}
-    return SetDotScalingVector{T,typeof(s)}(s)
+    function SetDotScalingVector{T}(s::MOI.AbstractSet) where {T}
+        return new{T,typeof(s)}(s)
+    end
 end
 
 function Base.getindex(s::SetDotScalingVector{T}, i::Base.Integer) where {T}
diff --git a/src/constraints.jl b/src/constraints.jl
index 65f6fd27dc..bba3a5a01a 100644
--- a/src/constraints.jl
+++ b/src/constraints.jl
@@ -95,6 +95,10 @@ An error indicating that the constant part of the function in the constraint
 """
 struct ScalarFunctionConstantNotZero{T,F,S} <: Exception
     constant::T
+
+    function ScalarFunctionConstantNotZero{T,F,S}(constant::T) where {T,F,S}
+        return new{T,F,S}(constant)
+    end
 end
 
 function Base.:(==)(