We show that the number of maximal independent sets of size exactly  k  in any graph of size  n  is at most  [ n/k ]^{k-(n mod k)} ([ n/k ] +1)^{n mod k}. For maximal independent sets of size at most  k  the same bound holds for  k  n/3  a bound of approximately  3^{n/3}  is given. All the bounds are exactly tight and improve Eppstein (2001) who give the bound  3^{4k-n}4^{n-3k}  on the number of maximal independent sets of size at most  k, which is the same for  n/