Firstly to those responsible, excellent web site.

I'm a DIY homeowner. I will be installing 3/4 x 2-1/4 white oak over 3/4 plywood subfloor, perpendicular to with 2x10 fir joists on 12 inch centers.
I have undercut my fireplace and door jambs, getting ready to start laying but I have two problems I'd appreciate some advice.

1. I have a hump about a foot in front of my fireplace for a bit over the width of the fireplace (6 feet). Its about 1 to 1.5 feet wide and runs parallel with the joists. The hump I figure is about 5/16 high. In any case too much to plane off the plywood. I'm planning to cut out the offending area, plane the problem joists and put in new plywood. Is this the best way to do this? One issue I see is that to minimize replaced area I may choose to lay the new plywood parallel to the joists, not optimal but I think my floor is actually quite strong (12 inch centers) so I think this is ok. Any comments.

2. I have a dip about 6 feet back from the hump. I've made a topographical map of the area. I runs more or less parallel to the joists (and the hump) Its about 1/4 inch deep for an area of about 1x3 feet and it tapers off to an 1/8 over about 2 or 3 feet in different directions. The overall shape is longer parallel to the joists. I thought about filling with plywood and tapering with paper but is seems quite a big area. I am considering how to do this by shimming from underneath. I'll be pulling up subfloor anyways for the hump. What do I use for shims? Do they need to cover the complete contact area between the plywood and the joist? One idea I had was to sister the joist and plane if required. But this seems like a lot of lumber and work. Any ideas.

Sorry for being so long winded and thanks in advance for any comments.

Both of your problems sound joist related. By that I mean, solid lumber floor joists used today are notoriuosly uneven. Your 2x10's could be off by up to 3/8 of an inch or even more. This is why so many builders of custom homes have gone to TJI's (trusses) because the quality of the milling has gotten so bad, along with lesser skilled carpenters who are supposed to check for that.
Anyway, how to fix.
1) This is what I would do. We're on the same page here. It's ok to change the direction of the plywood on a "patch". Just make sure you support the new and old section well and use nails (or screws) AND glue. BTW, 12" OC for floor joists is unusual. They must be spanned a little longer than normal to go with being that close.
2) For a 1/4" valley, I'd use fiberglass roofing singles and stack them up and taper them out as needed. Your subfloor and joists sound very stiff and solid so there is no worry there. And at 1/4" deep patch, you will still get most of the staple (nailing down the flooring) into the subfloor. I usually use my hammer tacker to staple down my shingles. This is an approved repair for fixing lows over wood subfloors with a 3/4" solid being nailed over it. You could use plywood and sand it down flush but more work. I just did this on a home where the addition subfloor did not meet up flush with the old subfloor. The roofing shingles fixed it in a jiffy, was inexpensive, and have had zero problems. OR, if you want to shim from underneath AND you have plenty of room to work, locate the offending joist(s) and drive a flat bar between the subfloor and low joist and pry up. Then drive wood shims in along the top of the joist(s) and refasten the subfloor (once it has been made flat) with screws. Simple but you do need room to work underneath. Oftentimes, there will be insulation in the way.
My long winded responce. Good luck.

Thanks Gary,
Got it done today. Ended up taking about 5/16 off (hand planner) of two joist, tapering towards the end of 9 feet. The spans are about 15 feet. Actually the whole thing it wasn't too hard to do (one days work) and now I have a nice flat surface.
We used a telepost to pry up the area where we wanted to shim, that worked really well. Otherwise it would have been kind of hard to pry up the plywood with only 12 inch centers.

Proteus