Hex and TRyan (and anyone else this method can help):
The key is to add equal air volume to T volume removed. Why equal air volume? Because it will get you as close as possible to your T volume with little or no guessing (you'll see what I mean). If you don't add any air, there will only be negative pressure and that's why it is so difficult (even nearly impossible) to draw the T up. That is also why the vial's air will often want to fill the barrel instead of the T at first ("the path of least resistance"). BUT by adding the (optimally, equal-to-dose) air volume to the vial first, you're creating positive pressure in the vial and that's what will push/propel that same volume of T into the negative pressure of the barrel (instead of negative vial pressure and negative barrel pressure, which = TPITA).
So:
1. Of course, begin by swabbing your vial top with alcohol (please don't ever neglect that) and continue steps 2 through 4 with the vial right-side up.
2. Take your draw syringe and draw up your dose amount in air. As in, just pull the plunger back until the rubber end is on your dose line (I do this with the cap still on but you can do it with it off if you want).
3. Put the syringe needle into the vial (BUT DON'T INJECT THE AIR YET!).
4. Make sure the needle is close to but not actually hitting the bottom of the vial.
5. Now turn the vial and syringe upside down (your fingers will want to touch the needle as you do this; don't let them).
6. Ensure the needle's end is in the vial's air (at the "top") and NOT in the T (hold it up against a light source if you have to); now inject the syringe air into the vial (as if you inject the air into the vial's T, it can bubble it and you don't want that. So I reiterate, ensure the needle's end is in the vial's air at the "top" before injecting the air).
7. You're going to pull the syringe barrel a little until the needle's end is a good way into the T.
8. Now pull the plunger back. Note, it is best to do this in one firm pull until you hit resistance. The point of resistance is where you will begin exceeding the volume of the air you had injected into the vial. You will continue to pull a bit beyond that resistance (not a lot though; you'll know when to stop) and:
9. Now *HOLD* the plunger where you pulled it to, until the vial's positive pressure continues to fill the barrel's empty negative pressure with the T "by itself" (you'll see what I mean). The pressure will stop trying to pull the plunger forward against your finger when the T has replaced that empty negative pressure in the barrel. IF it didn't fill completely, start pulling again but do it slow and steady this time otherwise it will start sucking the vial's air instead of the T and we don't want that PITA.
10. Now, with the vial and syringe still inverted, inject any excess T back into the vial until the plunger is on your dose line (IF there were any little air bubbles, they should be pushed back into the vial at this point. But IF there are somehow large bubbles you'll have to "tap out"/plunge out later).
11. Turn vial and filled syringe right-side up.
12. Remove and (carefully) recap syringe to prep injection site; and you know the rest.
When you've mastered that (you should rather quickly), not only will be it be ridiculously hassle-free to draw up but there should also only be an insignificantly tiny amount of air left in the barrel (i.e. no pushing the plunger before injection necessary); although it is always a good idea to turn the syringe upside down and flick it a few times to settle the tiny air bubble(s) up to the rubber-end (even if there doesn't seem to be any; they often hide near the needle). Another benefit is, you can essentially draw up with any needle gauge and skip using two different ones (unless you prefer a "virgin needle" to inject).
Other than that, the only time you should tilt a vial is when it is nearly empty. In that case you will tilt the vial, get the needle as close to the "bottom" as possible without it coming back out and you will also rotate the syringe until the needle bevel ("/") is parallel to the vial's side that has the T tilted towards it. Also, you might want to add more air than what you think is left to make it even simpler (but I wouldn't do that with a full/mostly full vial; only a nearly empty one). Otherwise, you will always want to keep the vial straight/level to avoid sucking up the vial's air.