How to prevent loose brake cables with a single pivot side-pull mechanism? I recently bought a second hand bike and am now tweaking it to my liking.
The bike has single pivot side-pull brakes, but it has a straight steering bar with regular brake levers (very similar, if not the same as this one).

I did not like the travel of the levers of the brake. I only had to squeeze them half a cm and the brakes would be fully applied already. I find it more comfortable to press the brake levers halfway (2-3 cm), it feels more controlled.

So I elongated the cable slightly at the brake, but now the cable travelling from my lever to the back wheel brake is hanging loose under the frame whenever it is not applied.

What should I do to increase the travel distance of the lever, but also make sure that the cable is not hanging loosely when not in use?
It's because you have a combination of brake levers designed for V-brakes and side pull brakes. V-brakes need more cable pull for the same effect, so your levers pull the cable too fast. 

The solution is to get levers designed for caliper brakes, something like for example this (note "Caliper or Canti Brake Lever System"): http://www.tektro.com/_english/01_products/01_prodetail.php?pid=69&amp;sortname=Lever&amp;sort=1&amp;fid=3. There are also adapters for cable pull issues, but they are made to solve the problem other way round and cost as much as simple brake levers.