Let f, g be two transcendental meromorphic functions in C, let P be a polynomial of uniqueness for meromorphic functions in C and let α be a small meromorphic function with regards to f and g. If f P (f) and g P (g) share α counting multiplicity, then we show that f = g provided that the multiplicity order of zeroes of P satisfy certain inequalities. There is no additional condition on α. We consider the particular case of entire functions.