No matter what name it has, the obvious and well-known powers of massage are to soothe your nervous system and reduce muscle aching and stiffness.  A fluffy, skin-deep massage isn't relaxing for most people, but neither is agonizing muscle abuse.  Your nervous system is neatly divided into halves:  you literally have a set of nerves for relaxing (parasympathetic), and a seperate set of nerves for action and panic (sympathetic).  A good massage will light up your chillaxing nerves like a Christmas tree and generally avoid setting off the panic nerves.  You know you're going into too much of the latter if you're gritting your teeth and flinching.

What makes a massage deep is not sheer force, but reasonable pressure in the right places at the right times.  The right places are key locations in muscles where muscle knots form, technically called "trigger points".  Trigger points are as common as pimples, but more lasting and uncomfortable.  They are the primary reason we get stiff and achy, and they can get shockingly unpleasant to live with.  Pressing on a trigger point generates a strange mixture of sensitivity and relief, what we call 'good pain' in the massage business.

Trigger points are unlikely to respond well to too much or too little pressure.  So, medium massage intensity is the usual maximum, and gentler is essential for some people.  Whatever the qualifications of your therapist, be assertive: ask for what you want, and do not tolerate too much pain, too fast, or pain with sharp, nasty quality.  And never hesitate to say, "a liitle to the left, please," or even show them on their own body where you think you need pressure. 

Help your therapist get to the "perfect spots."

Good massage always involves a little teamwork!