Does Distilled Water Freeze Clearer than Tap Water?

In my last set of icesperiments, I froze, melted, and refroze (tap) water to see if it became clearer on successive refreezings. It did not.

This time I compared tap water with distilled water to see if one would freeze more clearly than the other. I froze it, then melted and refroze it four more times. Though neither froze super clear, there were differences:

 

The tap water seems to freeze either clear or not clear, where the distilled water freezes in more of a bubble starburst. But in the end I'd say there's not enough of a difference to matter. 

After the break, a closeup of the distilled vs. tap ice.

The icesperiments shall continue!

In each of the below pics, tap water ice is on the left and distilled water ice is on the right.