diff --git a/Project.toml b/Project.toml
index 9b8e7d7..d47ba40 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,7 +11,7 @@ OpenBLAS32_jll = "656ef2d0-ae68-5445-9ca0-591084a874a2"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [compat]
-Cbc_jll = "=200.1000.1200"
+Cbc_jll = "=200.1000.1300"
 LinearAlgebra = "1"
 MathOptInterface = "1.7"
 OpenBLAS32_jll = "0.3.10"
diff --git a/src/MOI_wrapper/MOI_wrapper.jl b/src/MOI_wrapper/MOI_wrapper.jl
index 2264549..18d8c0f 100644
--- a/src/MOI_wrapper/MOI_wrapper.jl
+++ b/src/MOI_wrapper/MOI_wrapper.jl
@@ -393,12 +393,10 @@ function MOI.copy_to(dest::Optimizer, src::OptimizerCache)
             end
         end
     end
-    any_sos = false
     for (S, type) in ((MOI.SOS1{Float64}, 1), (MOI.SOS2{Float64}, 2))
         starts, indices, weights = Cint[], Cint[], Float64[]
         attr = MOI.ListOfConstraintIndices{MOI.VectorOfVariables,S}()
         for ci in MOI.get(src, attr)
-            any_sos = true
             push!(starts, Cint(length(weights)))
             f = MOI.get(src, MOI.ConstraintFunction(), ci)
             for x in f.variables
@@ -413,12 +411,6 @@ function MOI.copy_to(dest::Optimizer, src::OptimizerCache)
             Cbc_addSOS(dest, N, starts, indices, weights, Cint(type))
         end
     end
-    if any_sos && Cbc_getNumIntegers(dest) == 0
-        @warn(
-            "There are known correctness issues using Cbc with SOS " *
-            "constraints and no binary variables.",
-        )
-    end
     return _index_map(src)
 end
 
diff --git a/test/MOI_wrapper.jl b/test/MOI_wrapper.jl
index 9344d6d..672a30e 100644
--- a/test/MOI_wrapper.jl
+++ b/test/MOI_wrapper.jl
@@ -11,12 +11,9 @@ import Cbc
 import MathOptInterface as MOI
 
 function runtests()
-    for name in names(@__MODULE__; all = true)
-        if startswith("$(name)", "test_")
-            @testset "$(name)" begin
-                getfield(@__MODULE__, name)()
-            end
-        end
+    is_test(name) = startswith("$(name)", "test_")
+    @testset "$name" for name in filter(is_test, names(@__MODULE__; all = true))
+        getfield(@__MODULE__, name)()
     end
     return
 end
@@ -24,6 +21,7 @@ end
 function test_SolverName()
     @test MOI.get(Cbc.Optimizer(), MOI.SolverName()) ==
           "COIN Branch-and-Cut (Cbc)"
+    return
 end
 
 function test_supports_incremental_interface()
@@ -36,10 +34,6 @@ function test_runtests()
         MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
         MOI.instantiate(Cbc.Optimizer; with_bridge_type = Float64),
     )
-    MOI.Bridges.remove_bridge(
-        model.optimizer,
-        MOI.Bridges.Variable.ZerosBridge{Float64},
-    )
     MOI.set(model, MOI.Silent(), true)
     MOI.Test.runtests(
         model,
@@ -52,11 +46,6 @@ function test_runtests()
             ],
         ),
         exclude = [
-            # TODO(odow): upstream bug in Cbc
-            "test_linear_Indicator_",
-            "test_linear_SOS1_integration",
-            "test_linear_SOS2_integration",
-            "test_solve_SOS2_add_and_delete",
             # Can't prove infeasible.
             "test_conic_NormInfinityCone_INFEASIBLE",
             "test_conic_NormOneCone_INFEASIBLE",
@@ -199,193 +188,6 @@ function test_issue_187()
     return
 end
 
-# The test_linear_SOS1_integration test with the additional requirement that all
-# variables are integer.
-function test_SOS1()
-    model = MOI.Bridges.full_bridge_optimizer(
-        MOI.Utilities.CachingOptimizer(
-            MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
-            Cbc.Optimizer(),
-        ),
-        Float64,
-    )
-    config = MOI.Test.Config()
-    MOI.set(model, MOI.Silent(), true)
-    @test MOI.supports_constraint(
-        model,
-        MOI.VectorOfVariables,
-        MOI.SOS1{Float64},
-    )
-    @test MOI.supports_constraint(
-        model,
-        MOI.VariableIndex,
-        MOI.LessThan{Float64},
-    )
-    v = MOI.add_variables(model, 3)
-    MOI.add_constraint.(model, v, MOI.Integer())
-    @test MOI.get(model, MOI.NumberOfVariables()) == 3
-    vc1 = MOI.add_constraint(model, v[1], MOI.LessThan(1.0))
-    @test vc1.value == v[1].value
-    vc2 = MOI.add_constraint(model, v[2], MOI.LessThan(1.0))
-    @test vc2.value == v[2].value
-    vc3 = MOI.add_constraint(model, v[3], MOI.LessThan(2.0))
-    @test vc3.value == v[3].value
-    c1 = MOI.add_constraint(
-        model,
-        MOI.VectorOfVariables([v[1], v[2]]),
-        MOI.SOS1([1.0, 2.0]),
-    )
-    c2 = MOI.add_constraint(
-        model,
-        MOI.VectorOfVariables([v[1], v[3]]),
-        MOI.SOS1([1.0, 2.0]),
-    )
-    @test MOI.get(
-        model,
-        MOI.NumberOfConstraints{MOI.VectorOfVariables,MOI.SOS1{Float64}}(),
-    ) == 2
-    #=
-        To allow for permutations in the sets and variable vectors
-        we're going to sort according to the weights
-    =#
-    cs_sos = MOI.get(model, MOI.ConstraintSet(), c2)
-    cf_sos = MOI.get(model, MOI.ConstraintFunction(), c2)
-    p = sortperm(cs_sos.weights)
-    @test isapprox(cs_sos.weights[p], [1.0, 2.0], config)
-    @test cf_sos.variables[p] == v[[1, 3]]
-    objf =
-        MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([2.0, 1.0, 1.0], v), 0.0)
-    MOI.set(
-        model,
-        MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
-        objf,
-    )
-    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
-    @test MOI.get(model, MOI.ObjectiveSense()) == MOI.MAX_SENSE
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
-    MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == config.optimal_status
-    @test MOI.get(model, MOI.ResultCount()) >= 1
-    @test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
-    @test isapprox(MOI.get(model, MOI.ObjectiveValue()), 3, config)
-    @test isapprox(MOI.get(model, MOI.VariablePrimal(), v), [0, 1, 2], config)
-    MOI.delete(model, c1)
-    MOI.delete(model, c2)
-    MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == config.optimal_status
-    @test MOI.get(model, MOI.ResultCount()) >= 1
-    @test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
-    @test isapprox(MOI.get(model, MOI.ObjectiveValue()), 5, config)
-    @test isapprox(MOI.get(model, MOI.VariablePrimal(), v), [1, 1, 2], config)
-    return
-end
-
-# The test_linear_SOS2_integration test with the additional requirement that all
-# variables are integer.
-function test_SOS2()
-    model = MOI.Bridges.full_bridge_optimizer(
-        MOI.Utilities.CachingOptimizer(
-            MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
-            Cbc.Optimizer(),
-        ),
-        Float64,
-    )
-    config = MOI.Test.Config()
-    MOI.set(model, MOI.Silent(), true)
-    @test MOI.supports_constraint(
-        model,
-        MOI.VectorOfVariables,
-        MOI.SOS1{Float64},
-    )
-    @test MOI.supports_constraint(
-        model,
-        MOI.VectorOfVariables,
-        MOI.SOS2{Float64},
-    )
-    v = MOI.add_variables(model, 10)
-    @test MOI.get(model, MOI.NumberOfVariables()) == 10
-    bin_constraints = []
-    for i in 1:8
-        vc = MOI.add_constraint(model, v[i], MOI.Interval(0.0, 2.0))
-        @test vc.value == v[i].value
-        push!(bin_constraints, MOI.add_constraint(model, v[i], MOI.ZeroOne()))
-        @test bin_constraints[i].value == v[i].value
-    end
-    MOI.add_constraint(
-        model,
-        MOI.ScalarAffineFunction(
-            MOI.ScalarAffineTerm.([1.0, 2.0, 3.0, -1.0], v[[1, 2, 3, 9]]),
-            0.0,
-        ),
-        MOI.EqualTo(0.0),
-    )
-    MOI.add_constraint(
-        model,
-        MOI.ScalarAffineFunction(
-            MOI.ScalarAffineTerm.(
-                [5.0, 4.0, 7.0, 2.0, 1.0, -1.0],
-                v[[4, 5, 6, 7, 8, 10]],
-            ),
-            0.0,
-        ),
-        MOI.EqualTo(0.0),
-    )
-    MOI.add_constraint(
-        model,
-        MOI.VectorOfVariables(v[[1, 2, 3]]),
-        MOI.SOS1([1.0, 2.0, 3.0]),
-    )
-    vv = MOI.VectorOfVariables(v[[4, 5, 6, 7, 8]])
-    sos2 = MOI.SOS2([5.0, 4.0, 7.0, 2.0, 1.0])
-    c = MOI.add_constraint(model, vv, sos2)
-    #=
-        To allow for permutations in the sets and variable vectors
-        we're going to sort according to the weights
-    =#
-    cs_sos = MOI.get(model, MOI.ConstraintSet(), c)
-    cf_sos = MOI.get(model, MOI.ConstraintFunction(), c)
-    p = sortperm(cs_sos.weights)
-    @test isapprox(cs_sos.weights[p], [1.0, 2.0, 4.0, 5.0, 7.0], config)
-    @test cf_sos.variables[p] == v[[8, 7, 5, 4, 6]]
-    objf = MOI.ScalarAffineFunction(
-        MOI.ScalarAffineTerm.([1.0, 1.0], [v[9], v[10]]),
-        0.0,
-    )
-    MOI.set(
-        model,
-        MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
-        objf,
-    )
-    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
-    @test MOI.get(model, MOI.ObjectiveSense()) == MOI.MAX_SENSE
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
-    MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == config.optimal_status
-    @test MOI.get(model, MOI.ResultCount()) >= 1
-    @test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
-    @test isapprox(MOI.get(model, MOI.ObjectiveValue()), 15.0, config)
-    @test isapprox(
-        MOI.get(model, MOI.VariablePrimal(), v),
-        [0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 3.0, 12.0],
-        config,
-    )
-    for cref in bin_constraints
-        MOI.delete(model, cref)
-    end
-    MOI.add_constraint.(model, v, MOI.Integer())
-    MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == config.optimal_status
-    @test MOI.get(model, MOI.ResultCount()) >= 1
-    @test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
-    @test isapprox(MOI.get(model, MOI.ObjectiveValue()), 30.0, config)
-    @test isapprox(
-        MOI.get(model, MOI.VariablePrimal(), v),
-        [0.0, 0.0, 2.0, 2.0, 0.0, 2.0, 0.0, 0.0, 6.0, 24.0],
-        config,
-    )
-    return
-end
-
 """
     test_VariablePrimalStart()