The two dimensional oriented on-line strip packing problem requires items to be packed, one at a time, into a strip of fixed width and infinite height so as to minimise the total height of the packing. The items may neither be rotated nor overlap. In this paper, ten heuristics from the literature are considered for the special case where the items are rectangles. Six modifications to some of these heuristics are proposed, along with two entirely new shelf algorithms. The performances and efficiencies of all the algorithms are compared in terms of the total packing height achieved and computation time required in each case, when applied to 542 benchmark data sets documented in the literature.