diff --git a/ext/ExaModelsMOI.jl b/ext/ExaModelsMOI.jl
index 5a649404..a0498964 100644
--- a/ext/ExaModelsMOI.jl
+++ b/ext/ExaModelsMOI.jl
@@ -195,8 +195,17 @@ function copy_constraints!(c, moim, var_to_idx, T)
 
     con_types = MOI.get(moim, MOI.ListOfConstraintTypesPresent())
     for (F, S) in con_types
-        F <: MOI.VariableIndex && continue
         cis = MOI.get(moim, MOI.ListOfConstraintIndices{F,S}())
+        if F <: MOI.VariableIndex
+            for ci in cis
+                vi = MOI.get(moim, MOI.ConstraintFunction(), ci)
+                vartype, var_idx = var_to_idx[vi]
+                if vartype === :variable
+                    con_to_idx[ci] = var_idx
+                end
+            end
+            continue
+        end
         bin, offset =
             exafy_con(moim, cis, bin, offset, lcon, ucon, y0, var_to_idx, con_to_idx)
     end
diff --git a/test/JuMPTest/JuMPTest.jl b/test/JuMPTest/JuMPTest.jl
index 3dcd7845..5ff455a7 100644
--- a/test/JuMPTest/JuMPTest.jl
+++ b/test/JuMPTest/JuMPTest.jl
@@ -292,6 +292,15 @@ function runtests()
                     set_optimizer_attribute(jm, "print_level", 0)
                     optimize!(jm)
                     sol = value.(all_variables(jm))
+                    dsol = dual.(all_constraints(jm, include_variable_in_set_constraints = true))
+
+                    set_optimizer(jm, () -> ExaModels.Optimizer(ipopt))
+                    set_optimizer_attribute(jm, "print_level", 0)
+                    optimize!(jm)
+                    sol2 = value.(all_variables(jm))
+                    dsol2 = dual.(all_constraints(jm, include_variable_in_set_constraints = true))
+                    @test sol ≈ sol2 atol = 1.0e-6
+                    @test dsol ≈ dsol2 atol = 1.0e-6
 
                     for backend in BACKENDS
                         @testset "$backend" begin