Optimize your PNG pictures with tools like OptiPNG and PNGCrush to shave off some (kilo)bytes from APK size. Image optimization tips for websites apply here too: use appropriate picture formats, play with JPG compression, consider using binary transparencies instead of 8-bit transparencies etc.
If you ship big PNGs with alpha channel, you can trade some APK size for startup speed and use separate JPGs for RGB and A channels.
If you're making HTTP connections, check that your HTTP client utilizes content compression. If it caches received HTTP responses, check that it understands and uses caching-related HTTP headers correctly.
