The recent introduction of shaped pulses to Double Electron Electron Resonance (DEER) spectroscopy has led to significant enhancements in sensitivity through increased excitation bandwidths and improved control over spin dynamics. The application of DEER has so far relied on the presence of an incoherent pump channel to average out most undesired coherent effects of the pump pulse(s) on the observer spins. However, in fully coherent EPR spectrometers that are increasingly used to generate shaped pulses, the presence of coherent pump pulses means that these effects need to be explicitly considered. In this paper, we examine the effects of coherent rectangular and sech/tanh pump pulses in DEER experiments with up to three pump pulses. We show that, even in the absence of significant overlap of the observer and pump pulse excitation bandwidths, coherence transfer pathways involving both types of pulses generate spin echoes of considerable intensity. These echoes introduce artefacts, which, if not identified and removed, can easily lead to misinterpretation. We demonstrate that the observed echoes can be quantitatively modelled using a simple spin quantum dynamics approach that includes instrumental transfer functions. Based on an analysis of the echo crossing artefacts, we propose efficient phase cycling schemes for their suppression. This enables the use of advanced DEER experiments, characterized by high sensitivity and increased accuracy for long-distance measurements, on novel fully coherent EPR spectrometers.