I'm a bit confused about what you did. If there's a conversion going on here, you couldn't have used a sparse image, but rather a "direct" DMG.
If you want to back up with a sparse image, you should create it with Disk Utility, and then back up to it by selecting the volume it represents in the pop-up (rather than the file). Basically, you treat that like "real" disk...
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--Dave Nanian
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