Note: As I am answering from my personal experience, this primarily addresses the types of toilets I see day to day, which are Australian toilets. There are some differences around the world, your experiences and the type of toilet technology may differ in your region.
Some toilets have a 'dual-flush' button, allowing you to control the amount of water used for flushing (half or full flush):
If there's any leftover waste after a normal flush, attempt a half-flush to finish removing the waste.
Even if there's not a half-flush button, you can re-flush the toilet as it's filling the tank, to try and remove more of the waste without doing a full flush.
If your toilet doesn't have a dual-flush option, then using a bucket of water is a viable alternative as @Tms91 covers.