diff --git a/base/reflection.jl b/base/reflection.jl
index 6cb18c4e027ade..b24a2c7acbca11 100644
--- a/base/reflection.jl
+++ b/base/reflection.jl
@@ -188,11 +188,15 @@ function _methods(f::ANY,t::ANY,lim)
 end
 function _methods_by_ftype(t::ANY, lim)
     tp = t.parameters
+    nu = 1
     for ti in tp
         if isa(ti, Union)
-            return _methods(Any[tp...], length(tp), lim, [])
+            nu *= length(ti.types)
         end
     end
+    if 1 < nu <= 64
+        return _methods(Any[tp...], length(tp), lim, [])
+    end
     return ccall(:jl_matching_methods, Any, (Any,Int32), t, lim)
 end
 function _methods(t::Array,i,lim::Integer,matching::Array{Any,1})