Rest and recovery are just as important to building muscle as how hard you push during the exercises themselves. This is why the Complete Strength program has been designed with precise rest periods for each exercise. It is extremely important that you adhere to each exercise's rest period as listed in the workout tables. Doing so will ensure your body's best possible response to each movement.
Resting any less than the listed time will not allow your muscular and neural systems adequate recovery; this will ultimately limit the amount of weight you can lift. By the same token, taking too long of a rest period will allow the muscles to cool down and therefore reduce the reaction your body has for each set. It is therefore important to be very exact in timing your recoveries. I recommend bringing a stop-watch with you to each workout. Start the watch right as you complete each exercise and then start the next exercise as soon as the allotted rest time has run out on the watch.
For more information on why certain movements need more rest than others, please check here.