Ethylene pressure was used to vary the molecular architecture of amorphous polyethylenes synthesized with a palladium-bisimine catalyst. At low ethylene pressure, densely branched polymers are formed, and their melt rheology indicates no entanglement even though the weight-average molar mass is 370 000. Polymers produced at higher ethylene pressures have only slightly higher molar masses but show entanglement effects in their rheology. NMR suggests similar levels of short-chain branching (92-97 branches per 1000 carbons) in all the samples. A simple model of polymerization, based on the proposed "chain-walking" mechanism for this catalyst, is used to generate structures via computer simulation. While some of the experimental data are consistent with the predicted molecular structures, there are discrepancies in (i) the scaling of radius of gyration with molecular weight and (ii) the variation of terminal relaxation time with ethylene pressure, both of which suggest long-chain branching, which is not predicted by the computer simulation.