Reduce color.
Best results are often achieved by first tweaking the original color - using histograms and color range replacement. Lots of shades of one unimportant color vs few shades of a more important, but less pixel count, color can be manually tweaked (like a red highlight line vs a blue sky).
Crop out unimportant parts. For many formats, widths that are powers of 2 or multiples of 8 give more optimal results.
Don't forget to disable transparency if the format you are using supports it and you don't need it.
On a Windows PC - IrfanView is well featured for this work.