Preventing contractor upcharging

[Gustavus Adolphus]

I'm a reluctant real estate investor (I bought a rental property next to my house not because I want to be a landlord, but the previous owner agreed to sell for a low, low price, and I wanted to control the house next to mine, which was in rough shape and had some shady tenants). So I'm new to the game.

My issue is working with contractors. So far, it seems like almost every guy I've hired to do work on this house (which, again, has needed a lot of work -- from driveway repair to siding to roofing and more) upcharges as part of their pricing strategy. They'll quote a price for the job, sign a contract with me and then inevitably find all sorts of previously "unnoticed" problems once they begin working.

I get that there is always a certain amount of uncertainty regarding what you're going to find when you start opening up walls, etc., and that contractors need to be paid for significant amounts of extra labor or materials that go into a job. But the problem is that 1) the contractors seem to upcharge the job even for relatively minor extra work (like having to sister a few joists -- which takes maybe half an hour and $20 worth of material) and 2) it feels like I get gouged on pricing for all of the upcharged work. Once the contractors have half of the roof torn off and discover supposedly new issues that they did not know about when they gave me the original quote, I'm not in a good position to say no to the extra work. Nor do I have a realistic chance to shop around and see what other guys would charge to do that work. As a result, they get to charge basically whatever they want for the extra work. 

Any thoughts on dealing with this? I know vetting your contractor is part of the process, but I try, and it only seems to go so far. I get multiple bids for every job, I don't always hire the cheapest guy and I stay away from people who clearly underbid. In fact, I've tried to err toward people who give higher quotes, in the hope that there will be fewer surprises once the work is underway. But they all seem to take advantage of the situation once they are in the middle of the job.

Is this a problem with all contractors? Should I basically just factor in an extra 10-20% on every quote I get? Or is there a secret trick for finding guys who will avoid upcharging unless there is really a reasonable need for it (and in that case, give me a fair price for the extra work).