I was starting to think that powering the Pies was a very trial-and-error affair, but I just realised something important. They want regulated power supplies, because they like their voltage within narrow limits.
Unregulated power suppies tend to be cheaper, and what they do is chuck out what they hope is five volts (or whatever) and hope for the best. A regulated power supply is constantly measuring its output to ensure that its output is steady.
You can usually see whether a power supply is regulated or not, by reading what's on it carefully. If it doesn't say, then it may well be unregulated.