diff --git a/lib/matplotlib/axes.py b/lib/matplotlib/axes.py
index 82def00583ed..d2f48855343a 100644
--- a/lib/matplotlib/axes.py
+++ b/lib/matplotlib/axes.py
@@ -7861,7 +7861,19 @@ def hist(self, x, bins=10, range=None, normed=False, weights=None,
 
             x[0::2], x[1::2] = bins, bins
 
-            minimum = min(bins)
+            if log:
+                # setting a minimum of 0 results in problems for log plots
+                if normed:
+                    # for normed data, set to 0.1 * minimum data value
+                    # (gives 1 full dex for the lowest filled bin)
+                    ndata = np.array(n)
+                    minimum = (ndata[ndata>0].min())*0.1
+                else:
+                    # for non-normed data, set the min to 0.1, again so that
+                    # there is 1 full dex for the lowest bin
+                    minimum = 0.1
+            else:
+                minimum = min(bins)
 
             if align == 'left' or align == 'center':
                 x -= 0.5*(bins[1]-bins[0])