  The shape and diversity of dwarf galaxy rotation curves is at apparent odds
with dark matter halos in a $\Lambda$ Cold Dark Matter ($\Lambda$CDM)
cosmology. We use mock data from isolated dwarf galaxy simulations to show that
this owes to three main effects. Firstly, stellar feedback heats dark matter,
leading to a 'coreNFW' dark matter density profile with a slowly rising
rotation curve. Secondly, if close to a recent starburst, large HI bubbles push
the rotation curve out of equilibrium, deforming the rotation curve shape.
Thirdly, when galaxies are viewed near face-on, their best fit inclination is
biased high. This can lead to a very shallow rotation curve that falsely
implies a large dark matter core. All three problems can be avoided, however,
by a combination of improved mass models and a careful selection of target
galaxies. Fitting our coreNFW model to mock rotation curve data, we show that
we can recover the rotation curve shape, dark matter halo mass $M_{200}$ and
concentration parameter $c$ within our quoted uncertainties.
  We fit our coreNFW model to real data for four isolated dwarf irregulars,
chosen to span a wide range of rotation curve shapes. We obtain an excellent
fit for NGC 6822 and WLM, with tight constraints on $M_{200}$, and $c$
consistent with $\Lambda$CDM. However, IC 1613 and DDO 101 give a poor fit. For
IC 1613, we show that this owes to disequilibria and its uncertain inclination
$i$; for DDO 101, it owes to its uncertain distance $D$. If we assume $i_{\rm
IC1613} \sim 15^\circ$ and $D_{\rm DDO101} \sim 12$ Mpc, consistent with
current uncertainties, we are able to fit both galaxies very well. We conclude
that $\Lambda$CDM appears to give an excellent match to dwarf galaxy rotation
curves.
