diff --git a/test/runtests.jl b/test/runtests.jl
index ada005e..e1438d1 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -4,4 +4,5 @@ using TensorKit
 
 using QuadGK
 
-include("ising.jl")
+include("spaces.jl") # do they give spacemismatches?
+include("ising.jl") # do they give the correct results (with the expected accuracy)?
diff --git a/test/spaces.jl b/test/spaces.jl
new file mode 100644
index 0000000..184e92b
--- /dev/null
+++ b/test/spaces.jl
@@ -0,0 +1,36 @@
+println("--------")
+println(" spaces ")
+println("--------")
+
+# stuff different kinds of spaces into the schemes (and do 100 steps)
+A = classical_ising(Ising_βc)
+B = classical_ising_symmetric(Ising_βc)
+C = gross_neveu_start(0, 1, 0)
+
+models = [A, B, C]
+
+# The tests below check that the schemes don't lead to spacemismatches
+@testset "TRG - spaces" begin
+    for T in models
+        @eval begin
+            @test isa(run!(TRG($(T)), truncdim(7), maxiter(100)), Any)
+        end
+    end
+end
+
+@testset "BTRG - spaces" begin
+    for T in models
+        @eval begin
+            @test isa(run!(BTRG($(T)), truncdim(7), maxiter(100)), Any)
+        end
+    end
+end
+
+@testset "HOTRG - spaces" begin
+    for T in models
+        @eval begin
+            @test isa(run!(HOTRG($(T)), truncdim(7), maxiter(100)), Any)
+        end
+    end
+end
+