This work highlights the lack of unique solutions for regional groundwater flow models and quantifies the degree of freedom concerning hydraulic conductivities for models calibrated on measured hydraulic heads. The potential of 4He as an independent tracer at reducing the nonuniqueness problem is tested. Four different calibrated groundwater flow scenarios are presented for the Carrizo aquifer and surrounding formations in Texas. It is shown that variations of hydraulic conductivities up to 2 orders of magnitude in the Carrizo aquifer and overlying confining layer lead to similar calculated hydraulic heads. No clear-cut arguments are present to invalidate one groundwater flow scenario over a different one. In contrast, when tested with a 4He transport conceptual model, all groundwater flow scenarios except one failed to reproduce a coherent 4He transport behavior in the system. This study exemplifies possible future contributions of 4He at discerning which model most closely replicates natural conditions.