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You can use the old school process which is everywhere on here. Mike Sullivan has the best explaination for that. Very labor intensive and depending on the age of the shakes and whether they are fungi ridden, powerwasher can cause a lot of damage if not dialed in just right.

May want to rethink using SH, to little will bleach them but not clean them and it won't kill lichen. To much and you'll dry them out which won't result until about a year later.

Remember to have some form of water base oil to hydrate the wood.

Don't seal shakes as you seal in moisture and any algae or mildew that doesn't get cleaned. Also a powerwasher can drive the algae mildew fungi etc. into the wood if not done right.

Yes I have developed a solution that works well but don't care to have it all over the web. Much trial and error and cost went into getting the right combindation. I use 5 different ingredients in my solution. Based upon age, degree and type of infestation and whether old growth or new growth shakes/shingles the ingredients has to be mixed in different portions. There is no one mix for all. Many factors have to be considered.

First and formost, make sure the under felt is in good condition before agreeing to clean or you maybe replacing or repairing the roof. Because if the roof leaks after you clean, guess who the homeowner is going to say the last person was on the roof before it started leaking. Yes, you!

Just my two cents.