Purpose: Multi-echo gradient-recalled echo acquisitions for QSM enable optimizing the SNR for several tissue types through multi-echo (TE) combination or investigating temporal variations in the susceptibility (potentially reflecting tissue microstructure) by calculating one QSM image at each TE (TE-dependent QSM). In contrast with multi-echo QSM, applying Laplacian-based methods (LBMs) for phase unwrapping and background field removal to single TEs could introduce nonlinear temporal variations (independent of tissue microstructure) into the measured susceptibility. Here, we aimed to compare the effect of LBMs on the QSM susceptibilities in TE-dependent versus multi-echo QSM. Methods: TE-dependent recalled echo data simulated in a numerical head phantom and gradient-recalled echo images acquired at 3 T in 10 healthy volunteers. Several QSM pipelines were tested, including four distinct LBMs: sophisticated harmonic artifact reduction for phase data (SHARP), variable-radius sophisticated harmonic artifact reduction for phase data (V-SHARP), Laplacian boundary value background field removal (LBV), and one-step total generalized variation (TGV). Results from distinct pipelines were compared using visual inspection, summary statistics of susceptibility in deep gray matter/white matter/venous regions of interest, and, in the healthy volunteers, regional susceptibility bias analysis and nonparametric tests. Results: Multi-echo versus TE-dependent QSM had higher regional accuracy, especially in high-susceptibility regions and at shorter TEs. Everywhere except in the veins, a processing pipeline incorporating TGV provided the most temporally stable TE-dependent QSM results with an accuracy similar to multi-echo QSM. Conclusions: For TE-dependent QSM, carefully choosing LBMs can minimize the introduction of LBM-related nonlinear temporal susceptibility variations.