I wouldn't remove more than 1/3 of the tree's foliage. Start by removing any dead, broken, or rubbing branches. Then start working your way up the trunk. Stop before you reach the 1/3 "limit".

Pruning cuts made to river birches in winter are likely to result in bleeding when sap rises in spring. Although not usually a big problem, pruning from late spring through summer would lessen this potential problem.

The river birch is not usually all that susceptible to birch borers. That's more of a problem for other birch species.

be nice to know where you are ...

clear the trunk to 2 feet.. leaving no stubs ... go sit on your lawn chair for a week or two ... decide if you want more ...

no real hurry ...

after 2 weeks .... go 2 feet more ... observe for another week.. etc ...

take pix after first round.. let us critique ...

i would make it a 2 year project.. there really never is a hurry on a plant that can live 35 to 50 years or more ...

the oldest .. thickest are at the bottom.. it will get easier as you go up ...

buy a TREE SAW ... wet wood is not dry lumber.. it matters.. if you are going with sawzall ... buy a tree blade for that ..

google: proper limb removal ... read a few and ask questions.. if you need more guidance ...

your biggest problem.. will probably be getting rid of what you cut off ...

ken

Thank you all for your advice! Now I feel confident to start pruning around Labor Day and will view it as a multi-year program.

Ken--I'm very close to you in Northville, Michigan! Your advice is greatly appreciated as I am always hungry for new and better ways to enhance my landscape.

Edmund, if I were you and that close, I would insist on Ken giving me a personal guided tour of his place (-;