Neglected Plums

We've got 6 plum trees which were planted a number of years ago (6??) and have never been pruned. Looking for suggestions on how to get these trees back into shape so we can crop them! Last year we were surprised to get a crop, which were very small (no thinning) but quite tasty. How much can we safely prune back? What is good timing for pruning plums (zone 6b, about 30 miles west of Philadelphia)

I will be most interested in responses to this. I actually gave up growing plums a number of years ago because I never found a satisfactory way to prune them. Every cut will be responded to with a hair-brush full of new growth. In the light of what I have learned since, my sense is that the trick is to concentrate on heading cuts, and recognize that any, and every, pruning cut will provoke the development of a thicket of new wood. (I am not going back now to experiment any farther, because I now live in an area with massive black-knot pressure from surrounding wild plums and pin cherries, and it is easier to concede defeat up front.)

Broomholm Orchard
Zone 5b in Nova Scotia

What are the plum types/varieties? Diploids, Japanese, and prune-plums are all pruned (lol!) differently. I'll chime in when I get some more info. Also, is it possible to attach a picture of a more or less representative tree, as they stand now?

Mike Biltonen, Know Your Roots
Zone 5b in New York

Let me see if I can get some pictures tomorrow, as well as some more info. I didn't plant them myself, so I'm a bit unsure here....