The house I’m staying in only has a French Press, so I am pressing and it’s pretty great coffee but… 

Does a French press always leave some coffee sludge in the cup? 

Are my beans ground too fine? 

Do you use a French press daily?

In my experience, anything without a paper filter will let through some sediment - I've got a filterless pour over (a Pureover) that always lets some grains through. French press does similar. I've just learned to not drink the last fraction of coffee in my cup.

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Thanks, I was feeling the same but wondering if I was doing something wrong. Doesn’t bother me too much to get a little grit