@ P13 -
On our effected site, we have tried quite a bit to recover from the April 24th penalty. We continue to see an odd set of results in custom search engines (Engines that use a Google custom search box) which is why I asked.
Original URL - ranked 2nd for its intended visitor. The resulting page on our site is/was very detailed about the topic, and is often copied on other sites who temporarily rank for the phrase.
Changed URL - ranked for a few weeks as Ted mentions, then it just dropped to a -950, end of results type filter, where it resides with many other pages from our site.
Changed URL on custom search engines - Ranks top 10 as we would expect to find in Google main index. Same content, very few changes.
At one point, the URL we tested had dropped out of the top 10 in custom search as we continued to flatten out our onsite optimization. (reduced keywords, heading deoptimization, related phrases, reduced onsite links, reduced factors within our own control) When we started losing referrals from engines "Other Than Google" as well as dropping off the custom search pages, we decided to turn the focus back to our own visitors and what the other search engines liked. We put most of our original content optimization back into place. The page rose back to top 3 in custom search (search engines that use Google results, in some kind of unfiltered fashion), and we started gaining positions back in OTG engines.