Let \(\mu (I)\) denote the number of generators of the ideal I. It is well known that \(\mu (I^{k})\) is a polynomial for \(k\gg 0\) ; thus, \(\mu (I^{k})<\mu (I^{k+1})\) . Investigating \(\mu (I^{k})\) for small k has recently been of interest for many authors. In particular, some authors have constructed ideals with tiny powers, that is, \(\mu (I^{k+1})<\mu (I^{k})\) for small k. In this paper, we give a shorter and simpler construction of monomial ideals I with tiny powers, up to any given power; that is, \(\mu (I^{k+1})<\mu (I^{k})\) for all \(k\le l\) where l is any given positive integer l.
