diff --git a/src/Bridges/Constraint/functionize.jl b/src/Bridges/Constraint/functionize.jl
index 372c137250..526260d563 100644
--- a/src/Bridges/Constraint/functionize.jl
+++ b/src/Bridges/Constraint/functionize.jl
@@ -72,20 +72,6 @@ function MOI.delete(model::MOI.ModelLike, c::ScalarFunctionizeBridge)
 end
 
 # Constraints
-function MOI.set(
-    model::MOI.ModelLike,
-    ::MOI.ConstraintFunction,
-    c::ScalarFunctionizeBridge{T},
-    f::MOI.VariableIndex,
-) where {T}
-    MOI.set(
-        model,
-        MOI.ConstraintFunction(),
-        c.constraint,
-        MOI.ScalarAffineFunction{T}(f),
-    )
-    return
-end
 
 function MOI.get(
     model::MOI.ModelLike,
diff --git a/src/Bridges/bridge_optimizer.jl b/src/Bridges/bridge_optimizer.jl
index cb7cf23f9b..114f690988 100644
--- a/src/Bridges/bridge_optimizer.jl
+++ b/src/Bridges/bridge_optimizer.jl
@@ -1120,12 +1120,16 @@ function MOI.set(
 end
 
 # Constraint attributes
+
 function MOI.set(
     b::AbstractBridgeOptimizer,
     attr::MOI.ConstraintFunction,
     ci::MOI.ConstraintIndex{F},
-    func::F,
+    func,
 ) where {F}
+    if typeof(func) != F
+        throw(ArgumentError("Invalid type when setting ConstraintFunction."))
+    end
     if Variable.has_bridges(Variable.bridges(b))
         set = MOI.get(b, MOI.ConstraintSet(), ci)
         func, new_set = bridged_constraint_function(b, func, set)
@@ -1159,8 +1163,11 @@ function MOI.set(
     b::AbstractBridgeOptimizer,
     attr::MOI.ConstraintSet,
     ci::MOI.ConstraintIndex{MOI.VariableIndex,S},
-    value::S,
+    value,
 ) where {S<:MOI.AbstractScalarSet}
+    if typeof(value) != S
+        throw(ArgumentError("Invalid type when setting ConstraintSet."))
+    end
     _set_substituted(b, attr, ci, value)
     return
 end
@@ -1182,11 +1189,14 @@ function MOI.set(
     b::AbstractBridgeOptimizer,
     attr::MOI.ConstraintSet,
     ci::MOI.ConstraintIndex{<:MOI.AbstractScalarFunction,S},
-    set::S,
+    set,
 ) where {S<:MOI.AbstractScalarSet}
+    if typeof(set) != S
+        throw(ArgumentError("Invalid type when setting ConstraintSet."))
+    end
     if Variable.has_bridges(Variable.bridges(b))
         func = MOI.get(b, MOI.ConstraintFunction(), ci)
-        new_func, set = bridged_constraint_function(b, func, set)
+        _, set = bridged_constraint_function(b, func, set)
     end
     _set_substituted(b, attr, ci, set)
     return
@@ -1282,6 +1292,15 @@ function MOI.set(
     return
 end
 
+function MOI.set(
+    ::AbstractBridgeOptimizer,
+    ::MOI.ConstraintFunction,
+    ::MOI.ConstraintIndex{MOI.VariableIndex},
+    ::MOI.VariableIndex,
+)
+    return throw(MOI.SettingVariableIndexNotAllowed())
+end
+
 ## Getting and Setting names
 function MOI.get(
     b::AbstractBridgeOptimizer,
diff --git a/src/Test/test_modification.jl b/src/Test/test_modification.jl
index bd298942c6..21bb1150c2 100644
--- a/src/Test/test_modification.jl
+++ b/src/Test/test_modification.jl
@@ -932,3 +932,63 @@ function setup_test(
     )
     return
 end
+
+"""
+    test_modification_incorrect(model::MOI.ModelLike, config::Config)
+
+Test that constraint sets and functions cannot be set for the wrong type.
+"""
+function test_modification_incorrect(model::MOI.ModelLike, ::Config)
+    @requires MOI.supports_constraint(
+        model,
+        MOI.ScalarAffineFunction{Float64},
+        MOI.EqualTo{Float64},
+    )
+    x = MOI.add_variable(model)
+    c = MOI.add_constraint(
+        model,
+        MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x)], 0.0),
+        MOI.EqualTo(1.0),
+    )
+    @test_throws(
+        ArgumentError,
+        MOI.set(model, MOI.ConstraintSet(), c, MOI.LessThan(1.0)),
+    )
+    @test_throws(ArgumentError, MOI.set(model, MOI.ConstraintFunction(), c, x))
+    return
+end
+
+"""
+    test_modification_incorrect_VariableIndex(
+        model::MOI.ModelLike,
+        config::Config,
+    )
+
+Test that constraint sets cannot be set for the wrong set type, and that
+VariableIndex functions cannot be modified.
+"""
+function test_modification_incorrect_VariableIndex(
+    model::MOI.ModelLike,
+    ::Config{T},
+) where {T}
+    @requires MOI.supports_constraint(model, MOI.VariableIndex, MOI.LessThan{T})
+    @requires(
+        MOI.supports_constraint(model, MOI.VariableIndex, MOI.GreaterThan{T}),
+    )
+    x = MOI.add_variable(model)
+    c = MOI.add_constraint(model, x, MOI.GreaterThan(zero(T)))
+    @test_throws(
+        ArgumentError,
+        MOI.set(model, MOI.ConstraintSet(), c, MOI.LessThan(one(T))),
+    )
+    @test_throws(
+        ArgumentError,
+        MOI.set(model, MOI.ConstraintFunction(), c, one(T) * x),
+    )
+    y = MOI.add_variable(model)
+    @test_throws(
+        MOI.SettingVariableIndexNotAllowed(),
+        MOI.set(model, MOI.ConstraintFunction(), c, y),
+    )
+    return
+end
diff --git a/src/Test/test_objective.jl b/src/Test/test_objective.jl
index 1d02194b9c..87e7921f21 100644
--- a/src/Test/test_objective.jl
+++ b/src/Test/test_objective.jl
@@ -517,29 +517,3 @@ function test_objective_set_via_modify(model::MOI.ModelLike, config::Config)
     @test MOI.get(model, MOI.ListOfModelAttributesSet()) == [attr]
     return
 end
-
-"""
-    test_objective_incorrect_modifications(model::MOI.ModelLike, config::Config)
-
-Test that constraint sets cannot be set for the wrong set type, and that
-VariableIndex functions cannot be modified.
-"""
-function test_objective_incorrect_modifications(model::MOI.ModelLike, ::Config)
-    @requires MOI.supports_constraint(
-        model,
-        MOI.ScalarAffineFunction{Float64},
-        MOI.EqualTo{Float64},
-    )
-    x = MOI.add_variable(model)
-    c = MOI.add_constraint(
-        model,
-        MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x)], 0.0),
-        MOI.EqualTo(1.0),
-    )
-    @test_throws(
-        ArgumentError,
-        MOI.set(model, MOI.ConstraintSet(), c, MOI.LessThan(1.0)),
-    )
-    @test_throws(ArgumentError, MOI.set(model, MOI.ConstraintFunction(), c, x),)
-    return
-end
diff --git a/test/Bridges/Constraint/functionize.jl b/test/Bridges/Constraint/functionize.jl
index 4db63d07ec..158b3651fa 100644
--- a/test/Bridges/Constraint/functionize.jl
+++ b/test/Bridges/Constraint/functionize.jl
@@ -27,8 +27,6 @@ function test_scalar_functionize()
     y = MOI.add_variable(bridged_mock)
     ci = MOI.add_constraint(bridged_mock, x, MOI.GreaterThan(0.0))
     @test MOI.get(bridged_mock, MOI.ConstraintFunction(), ci) ≈ x
-    MOI.set(bridged_mock, MOI.ConstraintFunction(), ci, y)
-    @test MOI.get(bridged_mock, MOI.ConstraintFunction(), ci) ≈ y
     @test MOI.get(bridged_mock, MOI.ConstraintSet(), ci) == MOI.GreaterThan(0.0)
     MOI.set(bridged_mock, MOI.ConstraintSet(), ci, MOI.GreaterThan(1.0))
     @test MOI.get(bridged_mock, MOI.ConstraintSet(), ci) == MOI.GreaterThan(1.0)
diff --git a/test/Bridges/bridge_optimizer.jl b/test/Bridges/bridge_optimizer.jl
index f9aa41b8ab..79036e32bd 100644
--- a/test/Bridges/bridge_optimizer.jl
+++ b/test/Bridges/bridge_optimizer.jl
@@ -748,6 +748,20 @@ function test_recursive_model_objective(::Type{T} = Int) where {T}
     @test MOI.get(b, attr) ≈ x
 end
 
+function test_invalid_modifications()
+    model = MOI.Bridges.full_bridge_optimizer(
+        MOI.Utilities.Model{Float64}(),
+        Float64,
+    )
+    config = MOI.Test.Config()
+    MOI.Test.test_modification_set_function_single_variable(model, config)
+    MOI.empty!(model)
+    MOI.Test.test_modification_incorrect(model, config)
+    MOI.empty!(model)
+    MOI.Test.test_modification_incorrect_VariableIndex(model, config)
+    return
+end
+
 function test_ListOfConstraintAttributesSet()
     model = MOI.Bridges.Constraint.SplitInterval{Float64}(
         MOI.Utilities.Model{Float64}(),