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Let's say I have a 4-4-4-1 distribution. I have somewhere between 20 to 22 points.
What do I bid in this case? 2NT is not possible because of the singleton. 2C is not possible because what would be the rebid after the partner responds - any response promises a 5-carder.
What would be the right bid in this case?
I play Standard American 5 Card Major or 2/1.
Don't be afraid to downgrade the strength of a hand by 1 HCP when it is flawed for the call being made. Here, treat a (exactly) 20 HCP hand as just 19 and open 1D.
Remember that it is very rare for a distributional opening 1 bid to get passed out. Partner needs to have a hand with no excuse to respond; RHO needs a hand with no excuse to reopen; and LHO needs a hand with no decent 5-card suit. Just because you have a strong hand doesn't force you to open above the 1-level. With any doubt at all, just open 1D in tempo - Hands opening with a NT bid should be good examples of the type, not bad ones.
As I commented to steenbergh's answer:
Modern treatment (and rules!) now allows the 2NT opening with a singleton K as well [as with a singleton A]. This is an expert call, however, so should only be engaged in if partner is not going to react inappropriately when revealed.
If the singleton is an Ace (and an Ace only!) a lot of players will open this hand in 2NT. If it isn't an Ace, or if you very explicitly agree with your partner that 20-22 4-4-4-A is not 2NT, then just open in the lowest available 4-card and, if partner answers, jump to indicate points. If opponents start bidding, double*.
'Worst case' scenario is that everybody passes and you're playing a 1-level contract, but oftentimes partner's hand is very limited in these cases and a game-score is very improbable. You'd rather play a 1+2 then a 4-1, right?
(*) Note that opening and then doubling the opponents while Partner passed indicates a pretty strong hand on your side, and since you still have two unbid suits (or at least one if opponets are bidding one of your 4-cards) there is a good chance you will still find a fit with partner. Making this double a penalty is still an option for your partner, if he has length in opponents suit (probably your singleton).
