There is growing evidence of tri-exponential IVIM-DWI signal behavior in the liver. However, tri-exponential estimates often suffer from the instability associated with separating three decaying signal components sampled along a single dimension (i.e., b-value). In this work, standard monopolar and noise-optimized 2D (b-M1) data sampling schemes were acquired. From each acquisition, tri-exponential ROI-based fitting and a blood velocity standard deviation distribution (BVD) fitting method were performed. The estimated tri-exponential parameters were compared across acquisitions and fitting methods. Repeatable tri-exponential IVIM estimates were obtained using the 2D data sampling combined with BVD fitting. A new, physical tri-exponential model is also proposed.