Self-Inflating mats are made lighter and smaller-packing by both making the mat itself smaller, and by cutting perforations in the foam inside. The resulting mats (Thermarest Prolite and similar) fold in half lengthways before you roll them up.
A short (shoulder to knee) mat rolls up to about 11"X4" dia, and a regular length mat rolls up to 11"x5" dia, approximately.
The downsides compared to what you are using now are that they are only 1" thick, and the perforations in the foam means it's not as warm as the unperforated mats (OK down to something like 0° to 5°, depending on how you sleep).
The alternative is to use an air bed of some sort, as suggested above.
These are thicker and more comfortable on rough ground, but they do need blowing up.
Your options are
a) uninsulated, of various brands. Likely to be too cold outside of the summer.
b) Insulated (Exped Downmat or Synmat, or similar). These are warm, but blowing up by mouth will get dampness inside, which isn't good for the insulation, especially down.
c) Baffled (Thermarest Neoair or similar). These have the inside of bed divided into small compartments with heat reflective material. Similarly warm to insulated mats, but not as sensitive to the dampness in your breath if you don't use a pump.
All air mats, including self-inflating, are prone to failure, with either the shell of a self-inflating mat separating from the foam core (delaminating), or the baffles that hold an air bed in shape failing.
) and they're ready for use. Packing them after use is also a 30 second job.
