I hate wood screws. I used a hand drill on high and low settings, different bits, and a regular screwdriver, screwing regularly, and very carefully with each method, and still managed to break 6 wood screws. They broke way down in the holes, so I couldn't extract them, even with a screw extractor bit. I just had to move over, and drill another hole. I'm using drywall screws from now on. Feel free to comment with particular types, or brands of wood screw that don't constantly break, even when hand-screwing them in, like these pieces of crap from Home Depot do reliably. And yes - I used a countersink. I used 3 different kinds, specially made for the types of wood screws I have. The side panels here are a very hard maple, which certainly didn't help, but #8 and #10 screws shouldn't be weak enough to break when using a regular screwdriver, with slow, soft motions.

I broke off 2 screws here, and the only way to extract them, as they were too soft for my screw extractors, especially with no heads, was to drill around them with a tiny drill bit, used like a hand saw as it was spinning. Eventually the drill pulled the broken shafts out. I cut strips of wood with a box cutter to a rough circle, clamped them in the drill and ran it while holding a sanding sponge against them to make them more round (didn't have a dowel anywhere), then filled in glue, hammered them in, and used the flush-cut saw again to trim them flat. That saw is so handy for my screw-ups. Now I could redrill. I moved on to other doors while these pegs fillers dried.