It is quite possible to compress JPEG images - you can use IrfanView for a avriety of such compressions/conversions.
But you must realise that JPEG is a lossy format (data is lost in encoding), and A JPEG compressor would simply lose more data. A good compressor will use algorithms that result in size reduction while still maintaining (as far as possible) image quality at acceptable levels. But remember - you are losing quality.
I use irfan view and it works well.No need to use other softwares to compress jpg.
Gif’s can also be compressed a fair bit by reducing the no. of colours and trimming the frames.