Conventional coherent diffractive imaging (CDI) techniques rely on inversion of the two-dimensional phase problem in the fully coherent limit. Current work using synchrotrons has shown that by introducing a flexible parameter in a technique known as polyCDI, some reduced temporal coherence with relative bandwidth ∼3% can be tolerated for simple non-dispersive objects. We demonstrate that using a high harmonic source with modulated spectral characteristics, although the excellent temporal coherence properties are lost in detection, it is possible to increase the tolerable relative bandwidth to ∼20% by using the shrinkwrap technique and treating the data as if they were fully coherent but noisy. This reduces the integration time by a factor of ∼5. This result is critical for the future use of lab-based sources of extreme ultraviolet and soft x-rays for CDI of non-dispersive objects, and we anticipate that it will improve results at synchrotron sources also.