The transverse momentum of a colour-singlet massive particle in a hadronic collision is built up by two components, the perturbative effect of parton branchings and the nonperturbative effect of primordial kT. In previous studies of transverse momentum spectra for Z0 production at the Tevatron, the best fit to the experimental data are given when the primordial kT is set to a much higher value than what is expected considering the confinement of partons in the proton. We here investigate the possibility that the reason for this is that too few branchings are generated in showers, compared to the evolution used in the tuning of parton densities. This could then be compensated by increasing the value of Lambda_QCD. The study is done using the regular Pythia showering routines and a new algorithm where the branchings are ordered in transverse momentum pT^2 instead of virtuality Q^2.