diff --git a/src/Benchmarks/Benchmarks.jl b/src/Benchmarks/Benchmarks.jl
index 9efa017405..a31ae9f86c 100644
--- a/src/Benchmarks/Benchmarks.jl
+++ b/src/Benchmarks/Benchmarks.jl
@@ -232,4 +232,25 @@ end
     return model
 end
 
+@add_benchmark function copy_model(new_model)
+    model = new_model()
+    index = MOI.add_variables(model, 1_000)
+    cons = Vector{
+        MOI.ConstraintIndex{MOI.ScalarAffineFunction{Float64}, MOI.LessThan{Float64}}
+    }(undef, 1_000)
+    for (i, x) in enumerate(index)
+        cons[i] = MOI.add_constraint(
+            model,
+            MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x)], 0.0),
+            MOI.LessThan(1.0 * i)
+        )
+    end
+    
+    model2 = new_model()
+    MOI.copy_to(model2, model)
+    # MOI.copy_to(model2, model, filter_constraints=(x) -> x in cons[1:500])
+
+    return model2
+end
+
 end
diff --git a/src/Utilities/copy.jl b/src/Utilities/copy.jl
index 91736a80fa..7172bbec32 100644
--- a/src/Utilities/copy.jl
+++ b/src/Utilities/copy.jl
@@ -2,19 +2,25 @@
 
 """
     automatic_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike;
-                      copy_names::Bool=true)
+                      copy_names::Bool=true, 
+                      filter_constraints::Union{Nothing, Function}=nothing)
 
 Use [`Utilities.supports_default_copy_to`](@ref) and
 [`Utilities.supports_allocate_load`](@ref) to automatically choose between
 [`Utilities.default_copy_to`](@ref) or [`Utilities.allocate_load`](@ref) to
 apply the copy operation.
+
+If the `filter_constraints` arguments is given, only the constraints for which
+this function returns `true` will be copied. This function is given a 
+constraint index as argument. 
 """
 function automatic_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike;
-                           copy_names::Bool=true)
+                           copy_names::Bool=true, 
+                           filter_constraints::Union{Nothing, Function}=nothing)
     if supports_default_copy_to(dest, copy_names)
-        default_copy_to(dest, src, copy_names)
+        default_copy_to(dest, src, copy_names, filter_constraints)
     elseif supports_allocate_load(dest, copy_names)
-        allocate_load(dest, src, copy_names)
+        allocate_load(dest, src, copy_names, filter_constraints)
     else
         error("Model $(typeof(dest)) does not support copy",
               copy_names ? " with names" : "", ".")
@@ -108,7 +114,7 @@ Base.haskey(idxmap::IndexMap, vi::MOI.VariableIndex) = haskey(idxmap.varmap, vi)
 Base.keys(idxmap::IndexMap) = Iterators.flatten((keys(idxmap.varmap), keys(idxmap.conmap)))
 
 Base.length(idxmap::IndexMap) = length(idxmap.varmap) + length(idxmap.conmap)
-Base.iterate(idxmap::MOIU.IndexMap, args...) = iterate(Base.Iterators.flatten((idxmap.varmap, idxmap.conmap)), args...)
+Base.iterate(idxmap::IndexMap, args...) = iterate(Base.Iterators.flatten((idxmap.varmap, idxmap.conmap)), args...)
 
 """
     pass_attributes(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool, idxmap::IndexMap, pass_attr::Function=MOI.set)
@@ -242,16 +248,30 @@ end
 """
     copy_constraints(dest::MOI.ModelLike, src::MOI.ModelLike,
                      idxmap::IndexMap,
-                     cis_src::Vector{<:MOI.ConstraintIndex})
+                     cis_src::Vector{<:MOI.ConstraintIndex},
+                     filter_constraints::Union{Nothing, Function}=nothing)
 
 Copy the constraints `cis_src` from the model `src` to the model `dest` and fill
 `idxmap` accordingly. Note that the attributes are not copied; call
 [`pass_attributes`] to copy the constraint attributes.
+
+If the `filter_constraints` arguments is given, only the constraints for which
+this function returns `true` will be copied. This function is given a 
+constraint index as argument. 
 """
 function copy_constraints(dest::MOI.ModelLike, src::MOI.ModelLike,
                           idxmap::IndexMap,
-                          cis_src::Vector{<:MOI.ConstraintIndex})
+                          cis_src::Vector{<:MOI.ConstraintIndex},
+                          filter_constraints::Union{Nothing, Function}=nothing)
+    # Retrieve the constraints to copy.
     f_src = MOI.get(src, MOI.ConstraintFunction(), cis_src)
+
+    # Filter this set of constraints if needed before.
+    if filter_constraints !== nothing
+        filter!(filter_constraints, cis_src)
+    end
+
+    # Copy the constraints into the new model and build the map.
     f_dest = map_indices.(Ref(idxmap), f_src)
     s = MOI.get(src, MOI.ConstraintSet(), cis_src)
     cis_dest = MOI.add_constraints(dest, f_dest, s)
@@ -264,23 +284,41 @@ function pass_constraints(
     dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool, idxmap::IndexMap,
     single_variable_types, single_variable_indices,
     vector_of_variables_types, vector_of_variables_indices,
-    pass_cons=copy_constraints, pass_attr=MOI.set
+    pass_cons=copy_constraints, pass_attr=MOI.set;
+    filter_constraints::Union{Nothing, Function}=nothing
 )
+    # copy_constraints can also take a filter_constraints argument; however, filtering
+    # is performed within this function (because it also calls MOI.set on the constraints). 
+    # Don't pass this argument to copy_constraints/pass_cons to avoid a double filtering.
     for (S, cis_src) in zip(single_variable_types,
                             single_variable_indices)
+        if filter_constraints !== nothing
+            filter!(filter_constraints, cis_src)
+        end
         # do the rest in `pass_cons` which is type stable
         pass_cons(dest, src, idxmap, cis_src)
+
         cis_src = MOI.get(src, MOI.ListOfConstraintIndices{
             MOI.SingleVariable, S}())
+        if filter_constraints !== nothing
+            filter!(filter_constraints, cis_src)
+        end
         pass_attributes(dest, src, copy_names, idxmap, cis_src, pass_attr)
     end
 
     for (S, cis_src) in zip(vector_of_variables_types,
                             vector_of_variables_indices)
+        if filter_constraints !== nothing
+            filter!(filter_constraints, cis_src)
+        end
         # do the rest in `pass_cons` which is type stable
         pass_cons(dest, src, idxmap, cis_src)
+
         cis_src = MOI.get(src, MOI.ListOfConstraintIndices{
             MOI.VectorOfVariables, S}())
+        if filter_constraints !== nothing
+            filter!(filter_constraints, cis_src)
+        end
         pass_attributes(dest, src, copy_names, idxmap, cis_src, pass_attr)
     end
 
@@ -290,6 +328,9 @@ function pass_constraints(
     ]
     for (F, S) in nonvariable_constraint_types
         cis_src = MOI.get(src, MOI.ListOfConstraintIndices{F, S}())
+        if filter_constraints !== nothing
+            filter!(filter_constraints, cis_src)
+        end
         # do the rest in `pass_cons` which is type stable
         pass_cons(dest, src, idxmap, cis_src)
         pass_attributes(dest, src, copy_names, idxmap, cis_src, pass_attr)
@@ -317,14 +358,21 @@ function default_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike)
 end
 
 """
-    default_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool)
+    default_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool,
+                    filter_constraints::Union{Nothing, Function}=nothing)
 
 Implements `MOI.copy_to(dest, src)` by adding the variables and then the
 constraints and attributes incrementally. The function
 [`supports_default_copy_to`](@ref) can be used to check whether `dest` supports
 the copying a model incrementally.
+
+If the `filter_constraints` arguments is given, only the constraints for which
+this function returns `true` will be copied. This function is given a 
+constraint index as argument. 
 """
-function default_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool)
+function default_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike,
+                         copy_names::Bool, 
+                         filter_constraints::Union{Nothing, Function}=nothing)
     MOI.empty!(dest)
 
     vis_src = MOI.get(src, MOI.ListOfVariableIndices())
@@ -378,7 +426,8 @@ function default_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bo
     # Copy constraints
     pass_constraints(dest, src, copy_names, idxmap,
                      single_variable_types, single_variable_not_added,
-                     vector_of_variables_types, vector_of_variables_not_added)
+                     vector_of_variables_types, vector_of_variables_not_added,
+                     filter_constraints=filter_constraints)
 
     return idxmap
 end
@@ -678,13 +727,20 @@ function load_constraints(dest::MOI.ModelLike, src::MOI.ModelLike,
 end
 
 """
-    allocate_load(dest::MOI.ModelLike, src::MOI.ModelLike)
+    allocate_load(dest::MOI.ModelLike, src::MOI.ModelLike, 
+                  filter_constraints::Union{Nothing, Function}=nothing
+                  )
 
 Implements `MOI.copy_to(dest, src)` using the Allocate-Load API. The function
 [`supports_allocate_load`](@ref) can be used to check whether `dest` supports
 the Allocate-Load API.
+
+If the `filter_constraints` arguments is given, only the constraints for which
+this function returns `true` will be copied. This function is given a 
+constraint index as argument. 
 """
-function allocate_load(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool)
+function allocate_load(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool,
+                       filter_constraints::Union{Nothing, Function}=nothing)
     MOI.empty!(dest)
 
     vis_src = MOI.get(src, MOI.ListOfVariableIndices())
@@ -722,7 +778,8 @@ function allocate_load(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool
     pass_constraints(dest, src, copy_names, idxmap,
                      single_variable_types, single_variable_not_allocated,
                      vector_of_variables_types, vector_of_variables_not_allocated,
-                     allocate_constraints, allocate)
+                     allocate_constraints, allocate, 
+                     filter_constraints=filter_constraints)
 
     # Load variables
     load_variables(dest, length(vis_src))
@@ -743,7 +800,7 @@ function allocate_load(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool
     pass_constraints(dest, src, copy_names, idxmap,
                      single_variable_types, single_variable_not_allocated,
                      vector_of_variables_types, vector_of_variables_not_allocated,
-                     load_constraints, load)
+                     load_constraints, load, filter_constraints=filter_constraints)
 
     return idxmap
 end
diff --git a/test/Utilities/copy.jl b/test/Utilities/copy.jl
index 549668d9a8..ea79c4c2ca 100644
--- a/test/Utilities/copy.jl
+++ b/test/Utilities/copy.jl
@@ -256,3 +256,62 @@ MOI.supports_add_constrained_variable(::ReverseOrderConstrainedVariablesModel, :
     @test typeof(c1) == typeof(dest.constraintIndices[1])
     @test typeof(c2) == typeof(dest.constraintIndices[2])
 end
+
+@testset "Filtering copy: check based on index" begin
+    # Create a basic model. 
+    src = MOIU.Model{Float64}()
+    x = MOI.add_variable(src)
+    c1 = MOI.add_constraint(src, x, MOI.LessThan{Float64}(1.0))
+    c2 = MOI.add_constraint(src, x, MOI.GreaterThan{Float64}(0.0))
+
+    # Filtering function: the default case where this function always returns
+    # true is already well-tested by the above cases.
+    # Only keep the constraint c1.
+    f = (cidx) -> cidx == c1
+    
+    # Perform the copy.
+    dst = OrderConstrainedVariablesModel()
+    index_map = MOI.copy_to(dst, src, filter_constraints=f)
+
+    @test typeof(c1) == typeof(dst.constraintIndices[1])
+    @test length(dst.constraintIndices) == 1
+end
+
+mutable struct BoundModel <: MOI.ModelLike
+    # Type of model that only supports ≤ bound constraints. In particular, it does not support integrality constraints.
+    inner::MOIU.Model{Float64}
+    BoundModel() = new(MOIU.Model{Float64}())
+end
+
+MOI.add_variable(model::BoundModel) = MOI.add_variable(model.inner)
+MOI.add_constraint(model::BoundModel, f::MOI.AbstractFunction, s::MOI.LessThan{Float64}) = MOI.add_constraint(model.inner, f, s)
+MOI.supports_constraint(::BoundModel, ::Type{MOI.SingleVariable}, ::MOI.LessThan{Float64}) = true
+
+MOIU.supports_default_copy_to(::BoundModel, ::Bool) = true
+MOI.copy_to(dest::BoundModel, src::MOI.ModelLike; kws...) = MOIU.automatic_copy_to(dest, src; kws...)
+MOI.empty!(model::BoundModel) = MOI.empty!(model.inner)
+
+MOI.supports(::BoundModel, ::Type{MOI.NumberOfConstraints}) = true
+MOI.get(model::BoundModel, attr::MOI.NumberOfConstraints) = MOI.get(model.inner, attr)
+
+@testset "Filtering copy: check based on constraint type" begin
+    # Create a basic model. 
+    src = MOIU.Model{Float64}()
+    x = MOI.add_variable(src)
+    c1 = MOI.add_constraint(src, x, MOI.LessThan{Float64}(10.0))
+    c2 = MOI.add_constraint(src, x, MOI.Integer())
+
+    # Filtering function: get rid of integrality constraint.
+    f = (cidx) -> MOI.get(src, MOI.ConstraintSet(), cidx) != MOI.Integer()
+    
+    # Perform the unfiltered copy. This should throw an error (i.e. the implementation of BoundModel
+    # should be correct). 
+    dst = BoundModel()
+    @test_throws MOI.UnsupportedConstraint{MOI.SingleVariable, MOI.Integer} MOI.copy_to(dst, src)
+    
+    # Perform the filtered copy. This should not throw an error. 
+    dst = BoundModel()
+    MOI.copy_to(dst, src, filter_constraints=f)
+    @test MOI.get(dst, MOI.NumberOfConstraints{MOI.SingleVariable, MOI.LessThan{Float64}}()) == 1
+    @test MOI.get(dst, MOI.NumberOfConstraints{MOI.SingleVariable, MOI.Integer}()) == 0
+end