diff --git a/Project.toml b/Project.toml
index daae195..9d5e0b4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -10,7 +10,7 @@ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
-MathOptInterface = "0.9"
+MathOptInterface = "0.10"
 julia = "1"
 
 [extras]
diff --git a/src/conic_form.jl b/src/conic_form.jl
index b1ee86e..7c5a2ce 100644
--- a/src/conic_form.jl
+++ b/src/conic_form.jl
@@ -94,7 +94,7 @@ end
 function MOI.set(model::GeometricConicForm, ::MOI.ObjectiveSense, sense::MOI.OptimizationSense)
     model.sense = sense
 end
-variable_index_value(t::MOI.ScalarAffineTerm) = t.variable_index.value
+variable_index_value(t::MOI.ScalarAffineTerm) = t.variable.value
 variable_index_value(t::MOI.VectorAffineTerm) = variable_index_value(t.scalar_term)
 function MOI.set(model::GeometricConicForm{T}, ::MOI.ObjectiveFunction,
                  f::MOI.ScalarAffineFunction{T}) where {T}
@@ -141,14 +141,14 @@ function _load_constraints(model::GeometricConicForm, src, indexmap, cone_offset
     end
 end
 
-function MOI.copy_to(dest::GeometricConicForm{T}, src::MOI.ModelLike; copy_names::Bool=true) where T
+function MOI.copy_to(dest::GeometricConicForm{T}, src::MOI.ModelLike) where T
     MOI.empty!(dest)
 
     vis_src = MOI.get(src, MOI.ListOfVariableIndices())
     idxmap = MOIU.IndexMap()
 
     has_constraints = BitSet()
-    for (F, S) in MOI.get(src, MOI.ListOfConstraints())
+    for (F, S) in MOI.get(src, MOI.ListOfConstraintTypesPresent())
         i = get(dest.cone_types_dict, S, nothing)
         if i === nothing || F != MOI.VectorAffineFunction{T}
             throw(MOI.UnsupportedConstraint{F, S}())
@@ -167,10 +167,10 @@ function MOI.copy_to(dest::GeometricConicForm{T}, src::MOI.ModelLike; copy_names
     _load_variables(dest, length(vis_src))
 
     # Set variable attributes
-    MOIU.pass_attributes(dest, src, copy_names, idxmap, vis_src)
+    MOIU.pass_attributes(dest, src, idxmap, vis_src)
 
     # Set model attributes
-    MOIU.pass_attributes(dest, src, copy_names, idxmap)
+    MOIU.pass_attributes(dest, src, idxmap)
 
     # Load constraints
     offset = 0
diff --git a/src/matrix_input.jl b/src/matrix_input.jl
index cafe18f..e63af8e 100644
--- a/src/matrix_input.jl
+++ b/src/matrix_input.jl
@@ -64,7 +64,7 @@ struct LPStandardForm{T, AT<:AbstractMatrix{T}, VT <: AbstractVector{T}} <: Abst
     b::VT
 end
 
-function MOI.get(::LPStandardForm{T}, ::MOI.ListOfConstraints) where T
+function MOI.get(::LPStandardForm{T}, ::MOI.ListOfConstraintTypesPresent) where T
     return [(MOI.ScalarAffineFunction{T}, MOI.EqualTo{T}),
             (MOI.VectorOfVariables, MOI.Nonnegatives)]
 end
@@ -117,7 +117,7 @@ struct LPGeometricForm{T, AT<:AbstractMatrix{T}, VT <: AbstractVector{T}} <: Abs
     b::VT
 end
 
-function MOI.get(::LPGeometricForm{T}, ::MOI.ListOfConstraints) where T
+function MOI.get(::LPGeometricForm{T}, ::MOI.ListOfConstraintTypesPresent) where T
     return [(MOI.ScalarAffineFunction{T}, MOI.LessThan{T})]
 end
 const LT{T} = MOI.ConstraintIndex{MOI.ScalarAffineFunction{T}, MOI.LessThan{T}}
@@ -139,10 +139,10 @@ end
 
 abstract type LPMixedForm{T} <: AbstractLPForm{T} end
 
-function MOI.get(model::LPMixedForm{T}, ::MOI.ListOfConstraints) where T
+function MOI.get(model::LPMixedForm{T}, ::MOI.ListOfConstraintTypesPresent) where T
     list = Tuple{DataType, DataType}[]
     for S in [MOI.EqualTo{T}, MOI.Interval{T}, MOI.GreaterThan{T}, MOI.LessThan{T}]
-        for F in [MOI.SingleVariable, MOI.ScalarAffineFunction{T}]
+        for F in [MOI.VariableIndex, MOI.ScalarAffineFunction{T}]
             if !iszero(MOI.get(model, MOI.NumberOfConstraints{F, S}()))
                 push!(list, (F, S))
             end
@@ -176,14 +176,14 @@ function MOI.get(model::LPMixedForm{T}, ::MOI.ListOfConstraintIndices{MOI.Scalar
     ))
 end
 
-const VBOUND{S} = MOI.ConstraintIndex{MOI.SingleVariable, S}
-function MOI.get(model::LPMixedForm{T}, ::MOI.NumberOfConstraints{MOI.SingleVariable, S}) where {T, S <: LinearBounds{T}}
+const VBOUND{S} = MOI.ConstraintIndex{MOI.VariableIndex, S}
+function MOI.get(model::LPMixedForm{T}, ::MOI.NumberOfConstraints{MOI.VariableIndex, S}) where {T, S <: LinearBounds{T}}
     s = _sense(S)
     return count(MOI.get(model, MOI.ListOfVariableIndices())) do vi
         MOI.get(model, BoundSense(), vi) == s
     end
 end
-function MOI.get(model::LPMixedForm{T}, ::MOI.ListOfConstraintIndices{MOI.SingleVariable, S}) where {T, S <: LinearBounds{T}}
+function MOI.get(model::LPMixedForm{T}, ::MOI.ListOfConstraintIndices{MOI.VariableIndex, S}) where {T, S <: LinearBounds{T}}
     s = _sense(S)
     return collect(MOIU.LazyMap{VBOUND{S}}(
         Base.Iterators.Filter(MOI.get(model, MOI.ListOfVariableIndices())) do vi
@@ -194,7 +194,7 @@ function MOI.get(model::LPMixedForm{T}, ::MOI.ListOfConstraintIndices{MOI.Single
     end)
 end
 function MOI.get(::LPMixedForm, ::MOI.ConstraintFunction, ci::VBOUND)
-    return MOI.SingleVariable(MOI.VariableIndex(ci.value))
+    return MOI.VariableIndex(ci.value)
 end
 function MOI.get(model::LPMixedForm, ::MOI.ConstraintSet, ci::VBOUND)
     return _bound_set(model.v_lb[ci.value], model.v_ub[ci.value])
diff --git a/src/sparse_matrix.jl b/src/sparse_matrix.jl
index 57d42cc..8d8ba5d 100644
--- a/src/sparse_matrix.jl
+++ b/src/sparse_matrix.jl
@@ -39,7 +39,7 @@ function final_touch(A::SparseMatrixCSRtoCSC)
 end
 function _allocate_terms(colptr, indexmap, terms)
     for term in terms
-        colptr[indexmap[term.scalar_term.variable_index].value + 1] += 1
+        colptr[indexmap[term.scalar_term.variable].value + 1] += 1
     end
 end
 function allocate_terms(A::SparseMatrixCSRtoCSC, indexmap, func)
@@ -47,7 +47,7 @@ function allocate_terms(A::SparseMatrixCSRtoCSC, indexmap, func)
 end
 function _load_terms(colptr, rowval, nzval, indexmap, terms, offset)
     for term in terms
-        ptr = colptr[indexmap[term.scalar_term.variable_index].value] += 1
+        ptr = colptr[indexmap[term.scalar_term.variable].value] += 1
         rowval[ptr] = offset + term.output_index
         nzval[ptr] = -term.scalar_term.coefficient
     end
diff --git a/test/runtests.jl b/test/runtests.jl
index 7b23854..c37cc27 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -6,6 +6,7 @@ const MatOI = MatrixOptInterface
 const MOI = MatOI.MOI
 const MOIU = MatOI.MOIU
 const MOIB = MOI.Bridges
+const MOIT = MOI.Test
 
 
 const ATOL = 1e-4
@@ -45,11 +46,10 @@ const dense_A = [1.0 2.0
             v_ub = [Inf, Inf]
 
             function test_expected(form)
-                MOI.copy_to(MOI.Bridges.Constraint.Scalarize{Float64}(model), form, copy_names = false)
+                MOI.copy_to(MOI.Bridges.Constraint.Scalarize{Float64}(model), form)
                 MOI.set(model, MOI.VariableName(), MOI.VariableIndex.(1:2), var_names)
                 MOI.set(model, MOI.ConstraintName(), MOI.ConstraintIndex{MOI.ScalarAffineFunction{Float64}, MOI.EqualTo{Float64}}.(1:2), con_names)
-                MOI.set(model, MOI.ConstraintName(), MOI.ConstraintIndex{MOI.SingleVariable, MOI.GreaterThan{Float64}}.(1:2), vcon_names)
-                MOIU.test_models_equal(model, expected, var_names, [con_names; vcon_names])
+                MOIT.util_test_models_equal(model, expected, var_names, con_names)
             end
 
             @testset "change $(typeof(lp))" for lp in [
@@ -92,10 +92,10 @@ const dense_A = [1.0 2.0
             v_ub = [Inf, Inf]
 
             function test_expected(form)
-                MOI.copy_to(model, form, copy_names = false)
+                MOI.copy_to(model, form)
                 MOI.set(model, MOI.VariableName(), MOI.VariableIndex.(1:2), var_names)
                 MOI.set(model, MOI.ConstraintName(), MOI.ConstraintIndex{MOI.ScalarAffineFunction{Float64}, MOI.LessThan{Float64}}.(1:2), con_names)
-                MOIU.test_models_equal(model, expected, var_names, con_names)
+                MOIT.util_test_models_equal(model, expected, var_names, con_names)
             end
 
             @testset "change $(typeof(lp))" for lp in [