The exception is acetaminophen (paracetamol), commonly known as Tylenol -- which should be the pain-reliever of first resort because of its much lower incidence of negative side-effects.
In fact, the drug makers have caused it to be overlooked in favor of much more expensive medications and often claim that it isn't much more than a placebo -- because of the absence of negative side-effects.
While as effective in providing pain relief to the receptors in the brain, they are not as effective anti-inflammatories, which can be addressed separately by inflammation reducing movements. The worst thing about the NSAIDS and COX-2 inhibitors is the propensity to produce gastric upset and thus keeping the body always stressed out by those concerns.