  Dwarf spheroidal galaxies are excellent systems to probe the nature of
fermionic dark matter due to their high observed dark matter phase-space
density. In this work, we review, revise and improve upon previous phase-space
considerations to obtain lower bounds on the mass of fermionic dark matter
particles. The refinement in the results compared to previous works is realised
particularly due to a significantly improved Jeans analysis of the galaxies. We
discuss two methods to obtain phase-space bounds on the dark matter mass, one
model-independent bound based on Pauli's principle, and the other derived from
an application of Liouville's theorem. As benchmark examples for the latter
case, we derive constraints for thermally decoupled particles and
(non-)resonantly produced sterile neutrinos. Using the Pauli principle, we
report a model-independent lower bound of $m \geq 0.18\,\mathrm{keV}$ at 68% CL
and $m \geq 0.13\,\mathrm{keV}$ at 95% CL. For relativistically decoupled
thermal relics, this bound is strengthened to $m \geq 0.59\,\mathrm{keV}$ at
68% CL and $m \geq 0.41\,\mathrm{keV}$ at 95% CL, whilst for non-resonantly
produced sterile neutrinos the constraint is $m \geq 2.80\,\mathrm{keV}$ at 68%
CL and $m \geq 1.74\,\mathrm{keV}$ at 95% CL. Finally, the phase-space bounds
on resonantly produced sterile neutrinos are compared with complementary limits
from X-ray, Lyman-$\alpha$ and Big Bang Nucleosynthesis observations.
