Despite the abundance of studies on signal progression for arterial roads, most existing models for bandwidth maximization cannot concurrently ensure that the resulting delays will be at a desirable level, especially for urban arterials accommodating high turning volume at some major intersections or constrained by limited turning bay length. Extending from those models that aim to address delay minimization in the progression design, this study provides two enhanced progression maximization models for arterials with high turning volumes. The first model aims to select the signal plan that can produce the lowest total signal delays for all movements from the set of non-inferior offsets produced by MAXBAND. Failing to address the impact of potential turning bay spillback at some critical intersections under such a design may significantly degrade the quality of through progression and increase the overall delay. For this reason, the second model proposed in this study offers the flexibility to trade the progression bandwidths within a pre-specified level for the target delay reduction, especially for turning traffic. The evaluation results from both numerical analyses and simulation experiments have shown that both proposed models can produce the desirable level of performance when compared with the two benchmark models, MAXBAND and TRANSYT 16. The second model yielded the lowest average network delay of 117.2 seconds per vehicle (s/veh), compared with 121.7 s/veh with TRANSYT. Moreover, even its average delay of 141.8 s/veh for through vehicles is comparable with that of 141.2 s/veh by MAXBAND, which is designed mainly to benefit through-traffic flows.