diff --git a/examples/MINLPs/milp.jl b/examples/MINLPs/milp.jl
deleted file mode 100644
index 488fbd57..00000000
--- a/examples/MINLPs/milp.jl
+++ /dev/null
@@ -1,8 +0,0 @@
-function milp(; solver = nothing)
-    m = JuMP.Model(solver)
-
-    @variable(m, 0 <= objvar <= 20, Int)
-    @objective(m, Min, objvar)
-
-    return m
-end
diff --git a/src/MOI_wrapper/MOI_wrapper.jl b/src/MOI_wrapper/MOI_wrapper.jl
index ed0103af..ef295726 100644
--- a/src/MOI_wrapper/MOI_wrapper.jl
+++ b/src/MOI_wrapper/MOI_wrapper.jl
@@ -322,18 +322,6 @@ function MOI.add_constraint(model::Optimizer, vi::MOI.VariableIndex, set::SCALAR
     return MOI.ConstraintIndex{typeof(vi),typeof(set)}(vi.value)
 end
 
-function MOI.supports_constraint(
-    ::Optimizer,
-    ::Type{MOI.VariableIndex},
-    ::Type{MOI.Integer},
-)
-    return true
-end
-
-function MOI.add_constraint(model::Optimizer, f::MOI.VariableIndex, set::MOI.Integer)
-    model.var_type_orig[f.value] = :Int
-    return MOI.ConstraintIndex{typeof(f),typeof(set)}(f.value)
-end
 function MOI.supports_constraint(
     ::Optimizer,
     ::Type{MOI.VariableIndex},
@@ -457,6 +445,32 @@ function MOI.is_valid(model::Alpine.Optimizer, vi::MOI.VariableIndex)
     return 1 <= vi.value <= model.num_var_orig
 end
 
+function _get_bound_set(model::Alpine.Optimizer, vi::MOI.VariableIndex)
+    if !MOI.is_valid(model, vi)
+        throw(MOI.InvalidIndex(vi))
+    end
+    return _bound_set(model.l_var_orig[vi.value], model.u_var_orig[vi.value])
+end
+
+function MOI.is_valid(
+    model::Alpine.Optimizer,
+    ci::MOI.ConstraintIndex{MOI.VariableIndex,S},
+) where {S<:SCALAR_SET}
+    set = _get_bound_set(model, MOI.VariableIndex(ci.value))
+    return set isa S
+end
+
+function MOI.get(
+    model::Alpine.Optimizer,
+    ::MOI.ConstraintSet,
+    ci::MOI.ConstraintIndex{MOI.VariableIndex,S},
+) where {S<:SCALAR_SET}
+    if !MOI.is_valid(model, ci)
+        throw(MOI.InvalidIndex(ci))
+    end
+    return _get_bound_set(model, MOI.VariableIndex(ci.value))
+end
+
 # Taken from MatrixOptInterface.jl
 @enum ConstraintSense EQUAL_TO GREATER_THAN LESS_THAN INTERVAL
 _sense(::Type{<:MOI.EqualTo}) = EQUAL_TO
diff --git a/src/main_algorithm.jl b/src/main_algorithm.jl
index 4a3cdda8..20d27595 100644
--- a/src/main_algorithm.jl
+++ b/src/main_algorithm.jl
@@ -97,10 +97,6 @@ function load!(m::Optimizer)
     # Populate data to create the bounding MIP model
     recategorize_var(m)             # Initial round of variable re-categorization
 
-    :Int in m.var_type_orig && error(
-        "Alpine does not support MINLPs with generic integer (non-binary) variables yet!",
-    )
-
     # Solver-dependent detection
     _fetch_mip_solver_identifier(m)
     _fetch_nlp_solver_identifier(m)
diff --git a/test/test_algorithm.jl b/test/test_algorithm.jl
index 58554d7d..6400438e 100644
--- a/test/test_algorithm.jl
+++ b/test/test_algorithm.jl
@@ -1044,13 +1044,82 @@ end
     @test MOI.get(m, Alpine.NumberOfIterations()) == 0
 end
 
-@testset "Test integer variables" begin
+@testset "Test integer variable support via IntegerToZeroOneBridge" begin
     test_solver = optimizer_with_attributes(
         Alpine.Optimizer,
         "nlp_solver" => IPOPT,
         "mip_solver" => HIGHS,
         "minlp_solver" => JUNIPER,
     )
-    m = milp(solver = test_solver)
-    @test_throws "Alpine does not support MINLPs with generic integer (non-binary) variables yet!" JuMP.optimize!(m)
+
+    m = JuMP.Model(test_solver)
+
+    @variable(m, -10 <= objvar <= 20, Int)
+
+    @objective(m, Min, objvar)
+
+    JuMP.optimize!(m)
+
+    @test termination_status(m) == MOI.OPTIMAL
+    @test isapprox(objective_value(m), -10; atol = 1e-4)
+    @test isapprox(value(objvar), -10, atol = 1E-6)
+    @test MOI.get(m, Alpine.NumberOfIterations()) == 0
+end
+@testset "Test integer variable support 0" begin
+    test_solver = optimizer_with_attributes(
+        Alpine.Optimizer,
+        "nlp_solver" => IPOPT,
+        "mip_solver" => HIGHS,
+        "minlp_solver" => JUNIPER,
+    )
+
+    m = JuMP.Model(test_solver)
+
+    @variable(m, objvar, Int)
+    @constraint(m, -10 <= objvar)
+    @constraint(m, objvar <= 20)
+
+    @objective(m, Min, objvar)
+
+    @test_throws "Unable to use IntegerToZeroOneBridge because the variable MOI.VariableIndex(1) has a non-finite domain" JuMP.optimize!(
+        m,
+    )
+end
+@testset "Test integer variable support 1" begin
+    test_solver = optimizer_with_attributes(
+        Alpine.Optimizer,
+        "nlp_solver" => IPOPT,
+        "mip_solver" => HIGHS,
+        "minlp_solver" => JUNIPER,
+    )
+
+    m = JuMP.Model(test_solver)
+
+    @variable(m, -10 <= objvar, Int)
+    @constraint(m, objvar <= 20)
+
+    @objective(m, Min, objvar)
+
+    @test_throws "Unable to use IntegerToZeroOneBridge because the variable MOI.VariableIndex(1) has a non-finite domain" JuMP.optimize!(
+        m,
+    )
+end
+@testset "Test integer variable support 2" begin
+    test_solver = optimizer_with_attributes(
+        Alpine.Optimizer,
+        "nlp_solver" => IPOPT,
+        "mip_solver" => HIGHS,
+        "minlp_solver" => JUNIPER,
+    )
+
+    m = JuMP.Model(test_solver)
+
+    @variable(m, objvar <= 20, Int)
+    @constraint(m, -10 <= objvar)
+
+    @objective(m, Min, objvar)
+
+    @test_throws "Unable to use IntegerToZeroOneBridge because the variable MOI.VariableIndex(1) has a non-finite domain" JuMP.optimize!(
+        m,
+    )
 end