how do I zip a jpeg file to under 2mb

Well, can you not just scale the image(s) to be of slightly lower resolution?

If you want a more useful answer, you'll need to provide more info I suspect.

And if it's an option, there are more compression-efficient algorithms out there, such as bz2

Well without knowing what size the images are in the first place, its impossible to tell if they can be zipped to under 2MB.

Just right click on the file in Nautilus and select compress, then just follow what you see and you will have a zipped file.
The best option however would be to resize the images to a lower resolution if they are not intended for printing.

Hi,

JPEG is already a compressed file format:

http://en.wikipedia.org/wiki/JPEG

Thus compressing further will not result in a very significant reduction of size.
One valuable reason to compress JPEG files would be to include a bunch of JPEG files in one single archive for transportation or sending through the internet.

Regards

If you want to upload a photo to some webservice zipping will not help since most websites will not recognize the file anymore.
But you have two other options:
  - resize the image
  - use a higher JPEG compression value

The GIMP is a program that can do both for you. GIMP can be installed via the Software Center if it is not on your system yet.
To compress the file just open and save it a menu will pop up that asked for a compression value.
To reduce the size of an image open the file and choose Image → Scale Image... from the menu.

Be warned both will reduce the quaility of the image.

Indeed, I think you should do exactly what Thomas said!