diff --git a/Project.toml b/Project.toml
index 34ecd60..d21f742 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ITensorNetworksNext"
 uuid = "302f2e75-49f0-4526-aef7-d8ba550cb06c"
-version = "0.9.3"
+version = "0.9.4"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
 
 [workspace]
@@ -23,6 +23,12 @@ SimpleTraits = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
 SplitApplyCombine = "03a91e81-4c3e-53e1-a0a4-9c0c8f19dd66"
 TensorAlgebra = "68bd88dc-f39d-4e12-b2ca-f046b68fcc6a"
 
+[weakdeps]
+OMEinsumContractionOrders = "6f22d1fd-8eed-4bb7-9776-e7d684900715"
+
+[extensions]
+ITensorNetworksNextOMEinsumContractionOrdersExt = "OMEinsumContractionOrders"
+
 [compat]
 Adapt = "4.3"
 AlgorithmsInterface = "0.1"
@@ -35,6 +41,7 @@ LinearAlgebra = "1.10"
 MacroTools = "0.5.16"
 MatrixAlgebraKit = "0.6"
 NamedGraphs = "0.11, 0.12"
+OMEinsumContractionOrders = "1"
 Random = "1.10"
 SimpleTraits = "0.9.5"
 SplitApplyCombine = "1.2.3"
diff --git a/ext/ITensorNetworksNextOMEinsumContractionOrdersExt/ITensorNetworksNextOMEinsumContractionOrdersExt.jl b/ext/ITensorNetworksNextOMEinsumContractionOrdersExt/ITensorNetworksNextOMEinsumContractionOrdersExt.jl
new file mode 100644
index 0000000..abede5e
--- /dev/null
+++ b/ext/ITensorNetworksNextOMEinsumContractionOrdersExt/ITensorNetworksNextOMEinsumContractionOrdersExt.jl
@@ -0,0 +1,10 @@
+module ITensorNetworksNextOMEinsumContractionOrdersExt
+
+using ITensorNetworksNext: ITensorNetworksNext
+using OMEinsumContractionOrders: CodeOptimizer
+
+function ITensorNetworksNext.contraction_order(alg::CodeOptimizer, tn)
+    return ITensorNetworksNext._contraction_order(alg, tn)
+end
+
+end
diff --git a/src/contract_network.jl b/src/contract_network.jl
index b6b5215..92d69e5 100644
--- a/src/contract_network.jl
+++ b/src/contract_network.jl
@@ -52,7 +52,11 @@ struct LeftAssociative end
 function contraction_order(alg::LeftAssociative, tn)
     return prod(i -> symnameddims(i, Tuple(axes(tn[i]))), keys(tn))
 end
-function contraction_order(alg::EvaluationOrderAlgorithm, tn)
+# Internal implementation shared with the OMEinsumContractionOrders extension.
+function _contraction_order(alg, tn)
     s = contraction_order(Flat(), tn)
     return optimize_evaluation_order(s; alg)
 end
+function contraction_order(alg::EvaluationOrderAlgorithm, tn)
+    return _contraction_order(alg, tn)
+end
diff --git a/test/Project.toml b/test/Project.toml
index c45d412..796d3d1 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -11,6 +11,7 @@ ITensorPkgSkeleton = "3d388ab1-018a-49f4-ae50-18094d5f71ea"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MatrixAlgebraKit = "6c742aac-3347-4629-af66-fc926824e5e4"
 NamedGraphs = "678767b0-92e7-4007-89e4-4527a8725b19"
+OMEinsumContractionOrders = "6f22d1fd-8eed-4bb7-9776-e7d684900715"
 QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
@@ -36,6 +37,7 @@ ITensorNetworksNext = "0.9"
 ITensorPkgSkeleton = "0.3.42"
 MatrixAlgebraKit = "0.6"
 NamedGraphs = "0.11, 0.12"
+OMEinsumContractionOrders = "1"
 QuadGK = "2.11.2"
 Random = "1.10"
 SafeTestsets = "0.1"
diff --git a/test/test_contract_network.jl b/test/test_contract_network.jl
index a6cdb30..08927a0 100644
--- a/test/test_contract_network.jl
+++ b/test/test_contract_network.jl
@@ -4,6 +4,7 @@ using ITensorNetworksNext: Exact, ITensorNetwork, LeftAssociative, contract_netw
     linkinds, siteinds, tensornetwork
 using NamedGraphs.GraphsExtensions: arranged_edges, incident_edges
 using NamedGraphs.NamedGraphGenerators: named_grid
+using OMEinsumContractionOrders: GreedyMethod, TreeSA
 using TensorOperations: TensorOperations
 using Test: @test, @testset
 
@@ -20,7 +21,11 @@ using Test: @test, @testset
         ABCD_1 = contract_network([A, B, C, D]; alg = orderalg(LeftAssociative()))
         ABCD_2 = contract_network([A, B, C, D]; alg = orderalg(Greedy()))
         ABCD_3 = contract_network([A, B, C, D]; alg = orderalg(Optimal()))
+        ABCD_4 = contract_network([A, B, C, D]; alg = orderalg(GreedyMethod()))
+        ABCD_5 = contract_network([A, B, C, D]; alg = orderalg(TreeSA()))
         @test ABCD_1 == ABCD_2 == ABCD_3
+        @test ABCD_1 ≈ ABCD_4
+        @test ABCD_1 ≈ ABCD_5
     end
 
     @testset "Contract One Dimensional Network" begin
@@ -36,11 +41,15 @@ using Test: @test, @testset
         z1 = contract_network(tn; alg = orderalg(LeftAssociative()))[]
         z2 = contract_network(tn; alg = orderalg(Greedy()))[]
         z3 = contract_network(tn; alg = orderalg(Optimal()))[]
+        z4 = contract_network(tn; alg = orderalg(GreedyMethod()))[]
+        z5 = contract_network(tn; alg = orderalg(TreeSA()))[]
 
         @test abs(z1 - z2) / abs(z1) <= 1.0e3 * eps(Float64)
         @test abs(z1 - z3) / abs(z1) <= 1.0e3 * eps(Float64)
 
         @test z1 ≈ z2
         @test z1 ≈ z3
+        @test z1 ≈ z4
+        @test z1 ≈ z5
     end
 end