At our shop 1/3 of the shifts are overnights, so 1/3 of the typical shift burden is overnights. Exceptions for director/assistant director who may work a couple of overnights a month, but for most of the group it's about 5 a month. If this is important to you, you should think hard about it, no nights is very uncommon (although if you've been taking a big paycut to do so maybe you want to switch it up).
The bigger the shop the less common this is. For example, a really tiny single coverage shop might have two 12 hour shifts. So 1/2 of your shifts are overnight. A little larger single coverage shop might do three 8s- 1/3 are overnights. But as you add double and triple coverage, that coverage tends to be put onto the swing shifts, not the overnight shift. So one of our shops has five 8-hour physician shifts a day, starting at 6a, 10a, 2p, 6p, and 10p. 1/5 of the shifts are overnight. Between our two shops, 25% of our shifts are overnight shifts. So my "share" if I'm working 12 shifts a month, is 3 of them. Since we have some docs that work them exclusively, one of them might work his own share, my share, and the share of 2 or 3 other docs. Thus 3/4 of the docs aren't working nights.
If this doesn't exist at your facility, and you would like it to, I would submit that you can probably change things to make it possible. Bear in mind the financial price may be quite heavy to get another doc to work your share of nights though, but perhaps not as high as you might think. If an average shift pays $2000, and a night shift pays 25% more than an evening shift like ours does, and you are trading 4 night shifts for 4 evening shifts, then it really only costs you about $2K a month or $24K a year. Depending on where you are at in life, that may be trade you are willing to make. Earlier in my career, I made the trade going one direction. Now, as additional money has lower marginal utility, I make it in the other direction.
I suspect there are very few places this arrangement cannot be done, either formally or informally. Try it. Call up one of the other docs and see if he'll swap all your night shifts for his evening shifts. I assure you that most docs have their price when they really think about it.
