The speed bleeders are kewl. A little tip for using them, tho...carefully put a couple of wraps of teflon tape on the threads before installing them. This will keep them from allowing air into the system thru the threads, while they are loose for bleeding. I've seen some that come with a sealant of some kind on the threads, for the same reason.

Good luck with the bleeding...I have to say, next to standing on my head under the dash, bleeding the brakes is the worst job on one of these things...and I have a pressure bleeder!

Thanks guys.  Last night I put together my "homemade mason jar brake bleeding reservoir" and tonight I had to put some finishing touches on it (as in some more silicone around the brass fittings).  I'm not ready to give up on that method yet, but I am seriously considering buying the speed bleeders!  I'll keep ya posted!  

Not to me..............you do the right front before the left front. Always the furthest away until you finially get to the clostest. That's the way ebo taught me.............and I believe in ebo

That makes sense to me and almost all non-Corvette references on the 'net seem to agree: furthest from the M/C first (although front to back shouldn't matter since they're on different circuits).  But I double checked my Haynes and found this corroborating reference online:

Dave, the information in my shop manual (GM 1974 Sevice Manual) Says to bleed the the caliper NEAREST to the master cylinder FIRST, then the further out one. On a disc brake car while PRESSURE bleeding the book reads to hold open the proportioning valve with a tool J-23709
The manual reads "It is advisable to bleed one valve at a time to avoid allowing fluid level in resivoir to become dangerously low. The correct sequence is to bleed the valve, either front or rear system, nearest master cylinder first. This sequence expels air from lines and calipers or wheel cylinders nearest to the master cylinder first and eliminates the possibility that air in a line close to the master cylinder may enter a line farther away after it has been bled."
WOW, somehow my insticts must have been working. Two weeks ago I bench bled my new SSBC master cylinder. I then installed it on my power booster in the car. I then began bleeding the nearest caliper the (left) driver's side inboard bleeder. While doing this the outboard bleeder was spewing brake fluid. It is the Russell check valve style. The calipers are brand new SSBC 48mm 4 piston. I checked the inside seat, which looked ok. I then installed the original SSBC bleeder, which also spewed fluid. I'm using Silicone (Dot 5) fluid, which really doesn't matter. I contacted SSBC tech dept. to have the goofus tell me to tighten the bleeder more. What a joke. I finially connected with the sales dept. I spoke with a great guy. Long story-short he shot out a new caliper that I got on Wednesday. I painted it with three coats of VHT brake caliper blue paint and then one coat of clear. I expidited the drying between coats with a heat gun. Thursday I baked the whole caliper in mama's oven (she wasn't home) at 200 degrees for 20 minutes. I haven't put the caliper on yet. So this GM service manual WILL be the way that I finish the brake bleeding. Again, for some reason I started with the front driver side, which turns out right according to the manual. I hope this helps you with your project...............and GOOD LUCK to you.............You seem very meticulous, and that's the RIGHT WAY TO BE! You also really want to check on facts. I have to check the book a bit more before I just wing it. Keep us informed as to how it's going.

Thanks for the compliment!  I'm trying to be meticulous, but I've made plenty of mistakes along the way, too.  Fortunately the big thing I've learned from all those is to not rush into things without researching them first.  Like this brake thing.  So far, my "sucking method" well....sort of sucks.  I still have a soft pedal that goes all the way to the floor but with no obvious leaks.  I'm going to bug the wife tomorrow night to sit out in the garage and do some pedal pushing for me and see if I can firm things up that way.  And I still may spring for those speed bleeders, too.  Thanks again for the help and confirming that my Haynes manual is indeed correct according to the General.  

Thank you Dave for making me go back to the manual. I just installed my new SSBC caliper, on the left front. NOW FOR THE FUN PART. Can I borrow your wife to push the brake peddle? Just kidding I could use mine, but I have the Russell Check valve ones.