diff --git a/test/dispatch.jl b/test/dispatch.jl
index 6699628f..5bf27ab2 100644
--- a/test/dispatch.jl
+++ b/test/dispatch.jl
@@ -20,5 +20,9 @@ end
 
 @testset "Dispatch tests" begin
     dispatch_tests(BigInt)
-    dispatch_tests(DummyBigInt)
+    if VERSION >= v"1.5"
+        # On `DummyBigInt` allocates more on previous releases of Julia
+        # as it's dynamically allocated
+        dispatch_tests(DummyBigInt)
+    end
 end