Summary: It is shown that if is a finite-order meromorphic solution of the equation
where , , is a homogeneous difference polynomial with meromorphic coefficients, and and are polynomials in with meromorphic coefficients having no common factors such that
where denotes the order of zero of at with respect to the variable , then the Nevanlinna counting function satisfies . This implies that has a relatively large number of poles. For a smaller class of equations, a stronger assertion is obtained, which means that the pole density of is essentially as high as the growth of allows. As an application, a simple necessary and sufficient condition is given in terms of the value distribution pattern of the solution, which can be used as a tool in ruling out the possible existence of special finite-order Riccati solutions within a large class of difference equations containing several known difference equations considered to be of Painlevé type.