diff --git a/src/Utilities/cachingoptimizer.jl b/src/Utilities/cachingoptimizer.jl
index 776019fa64..c292586311 100644
--- a/src/Utilities/cachingoptimizer.jl
+++ b/src/Utilities/cachingoptimizer.jl
@@ -205,9 +205,9 @@ end
 
 function _reverse_index_map(src::IndexMap)
     dest = IndexMap()
-    sizehint!(dest.varmap, length(src.varmap))
-    _reverse_dict(dest.varmap, src.varmap)
-    _reverse_dict(dest.conmap, src.conmap)
+    sizehint!(dest.var_map, length(src.var_map))
+    _reverse_dict(dest.var_map, src.var_map)
+    _reverse_dict(dest.con_map, src.con_map)
     return dest
 end
 
diff --git a/src/Utilities/copy.jl b/src/Utilities/copy.jl
index bdb46e53ab..9d052820f9 100644
--- a/src/Utilities/copy.jl
+++ b/src/Utilities/copy.jl
@@ -39,143 +39,7 @@ end
 
 @deprecate supports_default_copy_to MOI.supports_incremental_interface
 
-"""
-    _index_to_variable(i::Int)
-
-Simply returns `MOI.VariableIndex(i)`. This is necessary to pass a function that
-creates the `VariableIndex` from an integer. If we pass `MOI.VariableIndex`
-julia understands is as a `DataType` and not a function, this leads to type
-instability issues.
-"""
-_index_to_variable(i) = MOI.VariableIndex(i)
-const DenseVariableDict{V} = CleverDicts.CleverDict{
-    MOI.VariableIndex,
-    V,
-    typeof(CleverDicts.key_to_index),
-    typeof(CleverDicts.index_to_key),
-}
-function dense_variable_dict(::Type{V}, n) where {V}
-    return CleverDicts.CleverDict{MOI.VariableIndex,V}(
-        MOI.index_value,
-        _index_to_variable,
-        n,
-    )
-end
-
-"""
-    struct IndexMap <: AbstractDict{MOI.Index,MOI.Index}
-        varmap::DenseVariableDict{MOI.VariableIndex}
-        conmap::DoubleDicts.MainIndexDoubleDict
-    end
-
-Dictionary-like object returned by [`MathOptInterface.copy_to`](@ref) that
-contains the mapping between variable indices in `varmap` and between
-constraint indices in `conmap`.
-"""
-struct IndexMap <: AbstractDict{MOI.Index,MOI.Index}
-    varmap::DenseVariableDict{MOI.VariableIndex}
-    conmap::DoubleDicts.MainIndexDoubleDict
-end
-
-function IndexMap(n = 0)
-    return IndexMap(
-        dense_variable_dict(MOI.VariableIndex, n),
-        DoubleDicts.IndexDoubleDict(),
-    )
-end
-
-function _identity_constraints_map(
-    model,
-    index_map::MOIU.DoubleDicts.IndexWithType{F,S},
-) where {F,S}
-    for ci in MOI.get(model, MOI.ListOfConstraintIndices{F,S}())
-        index_map[ci] = ci
-    end
-end
-
-"""
-    identity_index_map(model::MOI.ModelLike)
-
-Return an [`IndexMap`](@ref) that maps all variable and constraint indices of
-`model` to themselves.
-"""
-function identity_index_map(model::MOI.ModelLike)
-    vis = MOI.get(model, MOI.ListOfVariableIndices())
-    index_map = IndexMap(length(vis))
-    for vi in vis
-        index_map[vi] = vi
-    end
-    for (F, S) in MOI.get(model, MOI.ListOfConstraints())
-        _identity_constraints_map(model, index_map.conmap[F, S])
-    end
-    return index_map
-end
-
-"""
-    index_map_for_variable_indices(variables)
-
-This function does not add variables to the IndexMap.
-It simply initializes the IndexMap with a proper data struture.
-If the variable indices are contiguous and start from 1, then
-an optimized data structure with pre allocated memory is initialized.
-Otherwise the data structure will start empty and will try to
-keep using performant structure for as long as possible.
-"""
-function index_map_for_variable_indices(variables)
-    n = length(variables)
-    if all(i -> variables[i] == MOI.VariableIndex(i), 1:n)
-        return IndexMap(n)
-    else
-        return IndexMap()
-    end
-end
-
-Base.getindex(idxmap::IndexMap, vi::MOI.VariableIndex) = idxmap.varmap[vi]
-function Base.getindex(
-    idxmap::IndexMap,
-    ci::MOI.ConstraintIndex{F,S},
-) where {F,S}
-    return idxmap.conmap[ci]::MOI.ConstraintIndex{F,S}
-end
-
-function Base.setindex!(
-    idxmap::IndexMap,
-    vi1::MOI.VariableIndex,
-    vi2::MOI.VariableIndex,
-)
-    return Base.setindex!(idxmap.varmap, vi1, vi2)
-end
-function Base.setindex!(
-    idxmap::IndexMap,
-    ci1::MOI.ConstraintIndex{F,S},
-    ci2::MOI.ConstraintIndex{F,S},
-) where {F,S}
-    return Base.setindex!(idxmap.conmap, ci1, ci2)
-end
-
-function Base.delete!(idxmap::IndexMap, vi::MOI.VariableIndex)
-    return delete!(idxmap.varmap, vi)
-end
-function Base.delete!(idxmap::IndexMap, ci::MOI.ConstraintIndex)
-    return delete!(idxmap.conmap, ci)
-end
-
-function Base.haskey(idxmap::IndexMap, ci::MOI.ConstraintIndex)
-    return haskey(idxmap.conmap, ci)
-end
-Base.haskey(idxmap::IndexMap, vi::MOI.VariableIndex) = haskey(idxmap.varmap, vi)
-
-function Base.keys(idxmap::IndexMap)
-    return Iterators.flatten((keys(idxmap.varmap), keys(idxmap.conmap)))
-end
-
-Base.length(idxmap::IndexMap) = length(idxmap.varmap) + length(idxmap.conmap)
-function Base.iterate(idxmap::IndexMap, args...)
-    return iterate(
-        Base.Iterators.flatten((idxmap.varmap, idxmap.conmap)),
-        args...,
-    )
-end
+include("copy/index_map.jl")
 
 """
     pass_attributes(
@@ -467,7 +331,7 @@ function copy_constraints(
     s = MOI.get(src, MOI.ConstraintSet(), cis_src)
     cis_dest = MOI.add_constraints(dest, f_dest, s)
     for (ci_src, ci_dest) in zip(cis_src, cis_dest)
-        idxmap.conmap[ci_src] = ci_dest
+        idxmap[ci_src] = ci_dest
     end
     return
 end
@@ -610,17 +474,17 @@ function copy_free_variables(
     vis_src,
     copy_variables::F,
 ) where {F<:Function}
-    if length(vis_src) != length(keys(idxmap.varmap))
-        vars = copy_variables(dest, length(vis_src) - length(idxmap.varmap))
+    if length(vis_src) != length(idxmap.var_map)
+        vars = copy_variables(dest, length(vis_src) - length(idxmap.var_map))
         i = 1
         for vi in vis_src
-            if !haskey(idxmap.varmap, vi)
-                idxmap.varmap[vi] = vars[i]
+            if !haskey(idxmap, vi)
+                idxmap[vi] = vars[i]
                 i += 1
             end
         end
         @assert i == length(vars) + 1
-        @assert length(vis_src) == length(idxmap.varmap)
+        @assert length(vis_src) == length(idxmap.var_map)
     end
     return
 end
@@ -731,7 +595,7 @@ function default_copy_to(
     MOI.empty!(dest)
 
     vis_src = MOI.get(src, MOI.ListOfVariableIndices())
-    idxmap = index_map_for_variable_indices(vis_src)
+    idxmap = _index_map_for_variable_indices(vis_src)
 
     # The `NLPBlock` assumes that the order of variables does not change (#849)
     if MOI.NLPBlock() in MOI.get(src, MOI.ListOfModelAttributesSet())
diff --git a/src/Utilities/copy/allocate_load.jl b/src/Utilities/copy/allocate_load.jl
index a1e5431855..7494ff807c 100644
--- a/src/Utilities/copy/allocate_load.jl
+++ b/src/Utilities/copy/allocate_load.jl
@@ -323,7 +323,7 @@ function allocate_constraints(
         s = MOI.get(src, MOI.ConstraintSet(), ci_src)
         f_dest = map_indices(idxmap, f_src)
         ci_dest = allocate_constraint(dest, f_dest, s)
-        idxmap.conmap[ci_src] = ci_dest
+        idxmap[ci_src] = ci_dest
     end
 end
 
@@ -367,7 +367,7 @@ function allocate_load(
     MOI.empty!(dest)
 
     vis_src = MOI.get(src, MOI.ListOfVariableIndices())
-    idxmap = index_map_for_variable_indices(vis_src)
+    idxmap = _index_map_for_variable_indices(vis_src)
     constraint_types = MOI.get(src, MOI.ListOfConstraintTypesPresent())
     single_variable_types =
         [S for (F, S) in constraint_types if F === MOI.SingleVariable]
diff --git a/src/Utilities/copy/index_map.jl b/src/Utilities/copy/index_map.jl
new file mode 100644
index 0000000000..dddc54e2ad
--- /dev/null
+++ b/src/Utilities/copy/index_map.jl
@@ -0,0 +1,113 @@
+struct IndexMap <: AbstractDict{MOI.Index,MOI.Index}
+    var_map::CleverDicts.CleverDict{
+        MOI.VariableIndex,
+        MOI.VariableIndex,
+        typeof(CleverDicts.key_to_index),
+        typeof(CleverDicts.index_to_key),
+    }
+    con_map::DoubleDicts.MainIndexDoubleDict
+end
+
+"""
+    IndexMap(n::Int = 0)
+
+Dictionary-like object returned by [`MathOptInterface.copy_to`](@ref) that
+contains the mapping between variable indices in `.var_map` and between
+constraint indices in `.con_map`.
+"""
+function IndexMap(n::Int = 0)
+    var_map = CleverDicts.CleverDict{MOI.VariableIndex,MOI.VariableIndex}(
+        CleverDicts.key_to_index,
+        CleverDicts.index_to_key,
+        n,
+    )
+    con_map = DoubleDicts.IndexDoubleDict()
+    return IndexMap(var_map, con_map)
+end
+
+"""
+    _index_map_for_variable_indices(variables)
+
+This function does not add variables to the IndexMap.
+It simply initializes the IndexMap with a proper data struture.
+If the variable indices are contiguous and start from 1, then
+an optimized data structure with pre allocated memory is initialized.
+Otherwise the data structure will start empty and will try to
+keep using performant structure for as long as possible.
+"""
+function _index_map_for_variable_indices(variables)
+    n = length(variables)
+    if all(i -> variables[i] == MOI.VariableIndex(i), 1:n)
+        return IndexMap(n)
+    else
+        return IndexMap()
+    end
+end
+
+function _identity_constraints_map(
+    model,
+    map::MOIU.DoubleDicts.IndexWithType{F,S},
+) where {F,S}
+    for c in MOI.get(model, MOI.ListOfConstraintIndices{F,S}())
+        map[c] = c
+    end
+    return
+end
+
+"""
+    identity_index_map(model::MOI.ModelLike)
+
+Return an [`IndexMap`](@ref) that maps all variable and constraint indices of
+`model` to themselves.
+"""
+function identity_index_map(model::MOI.ModelLike)
+    variables = MOI.get(model, MOI.ListOfVariableIndices())
+    map = _index_map_for_variable_indices(variables)
+    for x in variables
+        map[x] = x
+    end
+    for (F, S) in MOI.get(model, MOI.ListOfConstraintTypesPresent())
+        _identity_constraints_map(model, map.con_map[F, S])
+    end
+    return map
+end
+
+Base.getindex(map::IndexMap, key::MOI.VariableIndex) = map.var_map[key]
+
+function Base.getindex(map::IndexMap, key::MOI.ConstraintIndex{F,S}) where {F,S}
+    return map.con_map[key]::MOI.ConstraintIndex{F,S}
+end
+
+function Base.setindex!(
+    map::IndexMap,
+    value::MOI.VariableIndex,
+    key::MOI.VariableIndex,
+)
+    return map.var_map[key] = value
+end
+
+function Base.setindex!(
+    map::IndexMap,
+    value::MOI.ConstraintIndex{F,S},
+    key::MOI.ConstraintIndex{F,S},
+) where {F,S}
+    return map.con_map[key] = value
+end
+
+Base.delete!(map::IndexMap, x::MOI.VariableIndex) = delete!(map.var_map, x)
+
+Base.delete!(map::IndexMap, c::MOI.ConstraintIndex) = delete!(map.con_map, c)
+
+Base.haskey(map::IndexMap, c::MOI.ConstraintIndex) = haskey(map.con_map, c)
+
+Base.haskey(map::IndexMap, x::MOI.VariableIndex) = haskey(map.var_map, x)
+
+function Base.keys(map::IndexMap)
+    return Iterators.flatten((keys(map.var_map), keys(map.con_map)))
+end
+
+Base.length(map::IndexMap) = length(map.var_map) + length(map.con_map)
+
+function Base.iterate(map::IndexMap, args...)
+    return iterate(Base.Iterators.flatten((map.var_map, map.con_map)), args...)
+end
diff --git a/test/Utilities/CleverDicts.jl b/test/Utilities/CleverDicts.jl
index 89e66c5fc9..d264d08d65 100644
--- a/test/Utilities/CleverDicts.jl
+++ b/test/Utilities/CleverDicts.jl
@@ -271,8 +271,11 @@ CleverDicts.index_to_key(::Type{MyKey}, index::Int64) = MyKey(index)
     @testset "convert" begin
         vals = [MathOptInterface.VariableIndex(-i) for i in 1:10]
         d = Dict(MathOptInterface.VariableIndex(i) => vals[i] for i in 1:10)
-        T = MathOptInterface.Utilities.DenseVariableDict{
-            MathOptInterface.VariableIndex,
+        T = CleverDicts.CleverDict{
+            MOI.VariableIndex,
+            MOI.VariableIndex,
+            typeof(CleverDicts.key_to_index),
+            typeof(CleverDicts.index_to_key),
         }
         c = convert(T, d)
         @test c isa T
diff --git a/test/Utilities/copy.jl b/test/Utilities/copy.jl
index 8b5b1b69ed..08883ee557 100644
--- a/test/Utilities/copy.jl
+++ b/test/Utilities/copy.jl
@@ -38,7 +38,7 @@ end
     cx = MOI.ConstraintIndex{MOI.SingleVariable,MOI.Integer}(1)
     cy = MOI.ConstraintIndex{MOI.SingleVariable,MOI.Integer}(2)
     map = MOIU.IndexMap(Dict(x => y), DoubleDicts.IndexDoubleDict())
-    map.conmap[cx] = cy
+    map[cx] = cy
     @test length(map) == 2
 end