We study the Howe correspondence for unipotent representations of irreducible dual pairs (G, G') = (U-m (F-q), U-n(F-q)) and (G, G') = (Sp(2m)(F-q), O-2n(epsilon) (F-q)), where F-q denotes the finite field with q elements (q odd) and epsilon = +/- 1. We show how to extract extrema] (i.e. minimal and maximal) irreducible subrepresentations from the image Theta(pi') of a unipotent representation pi' of G'. (C) 2019 Elsevier Inc. All rights reserved.