We do pumpernickel bread on a daily basis.
I do not recall seeing either rye or pumpernickel (sorry), however, that does not mean they do not have it as that is not what I was looking for. I would like to recommend that you try their pheasant bread. It's a white/wheat mix and is wonderful.
I'm sure they do. We are very pleased with the bread we buy and the wonderful friendly service.
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