With PSP you first reduce the colours to 256 using the "decrease colour depth" option on the Colours menu. Then save as windows or OS2 bitmap.

You can do something similar with Show (on the image processing button) or use the "force 256 colour" option in convim

Convim may be your best bet for both types. Just design them using PSP and then convert them to 256 colour or 16 bit 565 using convim

Thank you very much Martin, for all your help and all your useful programs.