Until now, I would have told you that was Houdini's only experience with Burlesque. But recently I found these remarkable clippings that show Houdini joined with the popular "Bowery Burlesquers" for a one-week engagement at the Gayety Theater in Washington, D.C. in February 1912. I'll let the clippings tell the story themselves.
One suspects the company made Houdini an offer he couldn't refuse. In fact, special perks may have been part of the deal, if this ad in the February 13, 1912 Washington Post is any indication.
During this week, Houdini escaped from Spanish Inquisition irons from the Washington D.C. War Museum. Papers reported that, "if the weather permits it is probable that he will dive from one of the bridges of the Potomac river." (He did not.)
UPDATE: Here's an item from the February 5, 1912 Atlanta Constitution that shed a little more light on why Houdini accepted this engagement.