How do I get accurate hydrometer readings?

So this weekend I brewed up my 8th extract batch or so. I'm turning out beer that's been solid overall, but I'm trying to refine my process so that I can go back to recipes with a pretty good degree of consistency. So far I've been pretty lax about taking hydrometer readings, when in doubt I usualy just let the beer do it's thing for an extra day or so before racking it.

But I decided I wanted to keep better notes and take regular samples. I've found that it's really tough to get an accurate hydrometer reading on an extract batch that I have to top off with water in the fermenter.

I've boiled about 3 gallons of wort, poured it on top of a gallon of water in the carboy and topped off with another gallon of water to make 5 and I take my reading of the finished beer, but the problem is that the water and the wort aren't fully mixed yet so the reading comes out extremely low. I tried to give the carboy a bit of a shake to mix it up, but once it's full it's so heavy I thought that risk of breaking it was too great. I'd wait a few hours for the solution to stabilize, but I don't want to give the wort any more time to attract an infection - once the wort is down to room temperature I want to pitch my yeast and be done with it.

Any ideas for getting a more accurate reading would be appreciated.

Not only do you want to mix it up well in order to get an accurate gravity reading, you also want to aerate it before you pitch your yeast. So mix it up good! I use a big spoon and stir, but that's using a 7 gallon bucket, not a carboy.

Just take the grav reading after aeration, and then again later after it has settled down some. You wont get an infection as long as you keep the wine thief and hydrometer sanitized. I have a 'holster' mounted to my workbench for quick draw hydrometer action. The holster is just PVC tube with a cap glued on one end, the other end has a removable pipe cap. I keep it filled with vodka so after washing off it goes in there to sanitize. I can then just dunk in the tube just prior to doing a grav reading.

beats mixing some sanitizer, and the whole thing cost $10 including the cheap 'McCormicks' vodka in a plastic bottle