  Purpose: The analysis of optimized spin ensemble trajectories for relaxometry
in the hybrid state.
  Methods: First, we constructed visual representations to elucidate the
differential equation that governs spin dynamics in hybrid state. Subsequently,
numerical optimizations were performed to find spin ensemble trajectories that
minimize the Cram\'er-Rao bound for $T_1$-encoding, $T_2$-encoding, and their
weighted sum, respectively, followed by a comparison of the Cram\'er-Rao bounds
obtained with our optimized spin-trajectories, as well as Look-Locker and
multi-spin-echo methods. Finally, we experimentally tested our optimized spin
trajectories with in vivo scans of the human brain.
  Results: After a nonrecurring inversion segment on the southern hemisphere of
the Bloch sphere, all optimized spin trajectories pursue repetitive loops on
the northern half of the sphere in which the beginning of the first and the end
of the last loop deviate from the others. The numerical results obtained in
this work align well with intuitive insights gleaned directly from the
governing equation. Our results suggest that hybrid-state sequences outperform
traditional methods. Moreover, hybrid-state sequences that balance $T_1$- and
$T_2$-encoding still result in near optimal signal-to-noise efficiency. Thus,
the second parameter can be encoded at virtually no extra cost.
  Conclusion: We provide insights regarding the optimal encoding processes of
spin relaxation times in order to guide the design of robust and efficient
pulse sequences. We find that joint acquisitions of $T_1$ and $T_2$ in the
hybrid state are substantially more efficient than sequential encoding
techniques.
