We study a proposed holographic representation of spread/Krylov complexity for states or operators dual to charged, composite and extended probes. Our analysis builds on the relation between the rate of spread complexity and the proper momentum of an infalling bulk excitation. A conserved Noether charge requires particular care: unitary spread complexity satisfies ${\dot{𝒞}}_K(0)=0$, and therefore the velocity conjugate to a fixed charge cannot be counted as an independent spreading direction. We consequently eliminate cyclic coordinates by a partial Legendre transform and compute the proper momentum from the fixed-charge Routhian. We first apply this prescription to an $R$-charged particle in AdS${}_5\times S^5$. The charge enters through the reduced effective mass and energy, while the resulting complexity has the required quadratic onset. We next study probes that are pointlike from the boundary perspective but possess non-trivial bulk structure. These are baryon-vertex configurations and giant gravitons. For the giant graviton the fixed-charge prescription retains the effects of the Born–Infeld and Wess–Zumino couplings without reintroducing the cyclic angular velocity into the proper momentum. We also analyse a fundamental string falling in AdS while stretched along a boundary spatial direction as a collective model of a non-local excitation. Within the rigid-probe Poincar'e-AdS examples considered here, the proper-momentum rate is linear at late times, whereas charges, compositeness and spatial extension affect its normalisation and its subleading or intermediate-time structure. We interpret this as a robust pattern in the tested class (not as a general universality theorem). The fixed-charge Routhian provides a candidate bulk counterpart of sector selection. An explicit symmetry-resolved boundary Lanczos construction remains an open problem.