Monitoring of respiratory mechanics is required for guiding patient-specific mechanical ventilation settings in critical care. Many models of respiratory mechanics perform poorly in the presence of variable patient effort. Typical modelling approaches either attempt to mitigate the effect of the patient effort on the airway pressure waveforms, or attempt to capture the size and shape of the patient effort. This work analyses a range of methods to identify respiratory mechanics in volume controlled ventilation modes when there is patient effort. The models are compared using 4 Datasets, each with a sample of 30 breaths before, and 2-3 minutes after sedation has been administered. The sedation will reduce patient efforts, but the underlying pulmonary mechanical properties are unlikely to change during this short time. Model identified parameters from breathing cycles with patient effort are compared to breathing cycles that do not have patient effort. All models have advantages and disadvantages, so model selection may be specific to the respiratory mechanics application. However, in general, the combined method of iterative interpolative pressure reconstruction, and stacking multiple consecutive breaths together has the best performance over the Dataset. The variability of identified elastance when there is patient effort is the lowest with this method, and there is little systematic offset in identified mechanics when sedation is administered.