We have implemented a code for Z + n jets production in ALPGEN, with Z decays into several final states, including l+ l- and t tbar. The MLM prescription is used for matching the matrix element with the parton shower, including in this way the leading soft and collinear corrections. In order to demonstrate its capabilities, we perform a combined analysis of Z -> t tbar and Z -> t tbar j production for a heavy leptophobic gauge boson. It is found that the effect of the extra jet cannot only be accounted for by a K factor multiplying the leading-order cross section. In fact, the combined analysis for Z -> t tbar and Z -> t tbar j presented improves the statistical significance of the signal by 25% (8.55 sigma versus 6.77 sigma for a Z mass of 1 TeV), compared with the results of an inclusive analysis carried out on the same sample of t tbar + t tbar j events.