There is growing interest in use of balanced steady-state free precession (bSSFP) imaging for simultaneous mapping of $$$T_1$$$, $$$T_2$$$ and off-resonance. An elegant ellipse fitting approach in the complex plane was recently proposed for parameter estimation from multiple phase-cycled acquisitions. Since this approach requires at least six phase-cycles, it can limit scan efficiency. Here, we propose a new technique that integrates a geometric solution with constrained ellipse fitting to enable mapping with only four phase-cycled acquisitions. The proposed method yields accurate $$$T_1$$$, $$$T_2$$$ and off-resonance maps while significantly improving scan efficiency.