Is there any downside of declaring function parameter as const pointer to const

A lot of books and experts say when talking about declaring functions/methods that you should put const everywhere you can unless you know that you need to modify that parameter. But I haven't seen much const pointer to const in the codes. Though if I have a pointer, and function dosn't need to modify neither pointer itself, nor pointed value, it seems to be a good choice to write this parameter as a const pointer to const. But mostly I've seen in such cases pointer to const is used. Is there any downside of declaring parameter as const pointer to const comparing with just pointer to const?