diff --git a/base/dict.jl b/base/dict.jl
index 2d4b24075381f..cc5c9efb6ada8 100644
--- a/base/dict.jl
+++ b/base/dict.jl
@@ -231,15 +231,16 @@ end
 
 function sizehint!(d::Dict{T}, newsz) where T
     oldsz = length(d.slots)
+    # limit new element count to max_values of the key type
+    newsz = min(newsz, max_values(T)::Int)
+    # need at least 1.5n space to hold n elements
+    newsz = cld(3 * newsz, 2)
     if newsz <= oldsz
         # todo: shrink
         # be careful: rehash!() assumes everything fits. it was only designed
         # for growing.
         return d
     end
-    # grow at least 25%
-    newsz = min(max(newsz, (oldsz*5)>>2),
-                max_values(T)::Int)
     rehash!(d, newsz)
 end