Sufficient conditions are obtained for the permanence of the following single species discrete model with feedback control: {N(n + 1) = N (n) exp [r(n) (1 - N(n - m)/k(n) - c(n)mu(n))], {Delta mu(n) = -a(n)mu(n) + b(n) N(n - m), where a : Z -> (0, 1), c, k, r, b : Z -> R+ are all nonnegative functions and m is a positve constant. (c) 2006 Elsevier Ltd. All rights reserved.