JPEG compression algorithm to be stopped if set data size reached?

Hello,

Is it possible to manage the compression procedure in that way that the compression is done step by step, with increasing quality until certain data size is reached, then the compression should stop?

I mean the size of the image depends on the content of the image. If the content of the image has got many different textures, then it has got larger size as the one with large smooth areas.

However, I would like to have a data container with a fixed size, thus the compression should be stopped earlier of later with regard to the occupied data size.

Could you advice me or tell me, which jpeg compression library supports it or some algorithm that can do it? Thanks.

Please don't double post. Thanks.