[Don't believe what I say, as I am fairly new to boxing (4 months training) -- although I do have quite a bit more martial arts, fighting, and specifically Systema (Russian Martial Arts) experience -- but if it gives you some ideas and they prove to work FOR YOU then use them.]

This question was asked on another forum, and because I am a pressure fighter -- all things being equal I will go forward consistently and successfully even against boxers who are (somewhat at least) better than I am -- I offered this answer which met with quite a bit of approval.

The biggest mistakes people make that lets the pressure fighter continue to come forward and even overwhelm them include:
  1. Leaning back as you back pedal -- you MUST keep your balance and form no matter the pressure. (I don't mean you cannot OCCASIONALLY pull back to slip a punch, but rather that you must not get back on your heels with your OWN weight and balance HELPING to pressure you backwards.
  2. Going straight back -- take no more than one back step (at least at first until you get the idea) before you start to sidestep or circle -- move laterally and try to let the pressure evaporate against the place you WERE standing
  3. Not throwing enough -- use your jab primarily, but use anything you can throw, don't just back up and let him keep coming -- you have to make him respect you, and primarily it is best to make him respect your jab or suffer the consequences for failing to do that.

    Do not let him just keep swarming into your area without getting hit and paying a price.
  4. Forgetting to parry, block, slip, fade, and duck -- you MUST use your good defensive skills, especially parrying.
  5. failing to Box -- use all of your boxing skills -- this one is harder, no quick fix, but it comes from doing all of those things above AND continuing to use your basics.

    Move, Hit, Maintain form/balance, stay relaxed, use good defense, etc.
Remember, I am no expert, but this makes applying pressure much harder for guys like me, and you want (you NEED) to stop him from doing that.

Please feel free to suggest changes, improvements, criticisms as I am trying to learn as much as possible....

For instance:

The very day after I posted this, Coach set me several problems by using restrictions in the ring. Effectively, he fixed my choices so that I (who normally go forward) was required to back up and still hold the center of the ring.

Because I had spent time thinking through the above answer (and because Coach had spent hours over the past months instilling the basics, especially of parrying, in me) it turned out that I was able to solve those problems immediately. By trying to help others, I had accidentally helped myself and done my homework EVEN BEFORE getting the assignment. That's pretty cool!
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HerbM