Replacing a few bricks at top of chimney

Yesterday I had a contractor come out to give me a bid on fixing my fireplace and brick chimney. He said he couldn't really tell until I had the soot cleaned out. He said as far as fixing the chimney, a lot depends on whether it's "cracked." I asked how you can tell and he asked me if the chimney feels solid when you try to shake it from the roof, or if it wobbles. I asked him if he wanted to accompany me up there and see and he said he'd forgotten to wear his shoes. He had sandals on.
Later, after he left, I was on the roof to check on some other things and I thought I'd check out the chimney and tried to see if it was solid or wobbly, like he said. In doing so, I evidently loosened one side of the top 3 layers of bricks. Maybe he was smart to not be wearing his shoes! Can I repair these by removing the bricks, cleaning them and resetting them with some brick mortar? I'm not ready to have the whole chimney done now because the house needs a foundation job, but if an earthquake hit now, the bricks would damage my roof and would then be apt to fall on my car. Thanks for the help.
Dan
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repair. Since over time, top courses are likely to suffer weakened or dissolved mortar joints due to water influx and freeze/thaw cycles, you might consider fitting a galvanized steel cap once the brick is repointed, so water will be directed away from the top chimney bricks in the future.
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