In the maximum cover problem, we are given a collection of sets over a ground set of elements and a positive integer w, and we are asked to compute a collection of at most w sets whose union contains the maximum number of elements from the ground set. This is a fundamental combinatorial optimization problem with applications to resource allo- cation. We study the simplest APX-hard variant of the problem where all sets are of size at most 3 and we present a 6=5-approximation algo- rithm, improving the previously best known approximation guarantee. Our algorithm is based on the idea of ¯rst computing a large packing of disjoint sets of size 3 and then augmenting it by performing simple local improvements.