  We introduce supersymmetric indices for four-dimensional gauge theories
defined on $\mathscr O \times S^1$, where $\mathscr O $ is a circle bundle over
the weighted complex projective line informally known as spindle. Trivial
fibrations yield a four-dimensional version of the spindle index, which we
obtain by applying localization to partition functions of theories on the
direct product of a spindle and a two-dimensional torus. Conversely,
non-trivial fibrations lead to the branched lens index, which we compute by
localizing theories on the direct product of a circle and a branched covering
of the lens space, possibly endowed with conical singularities. The branched
lens index encompasses the maximally refined four-dimensional lens index as a
special case.
