Answer: Prunus laurocerasus 'Schipkaensis', or Skip Laurel, is one of the hardiest laurels around. They thrive in full sunshine and well draining soil. The spots you describe could be fungal or bacterial spots, but I'm not sure which. However, you can prune away the infected foliage which will not only remove it from the garden but will also encourage healthy new grow on your laurels. Hope this solves the problem.
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