  Power-law distributions are a near universal feature of energetic particle
spectra in the heliosphere. Anomalous Cosmic Rays (ACRs), super-Alfv\'enic ions
in the solar wind and the hardest energetic electron spectra in flares all have
energy fluxes with power-laws that depend on energy $E$ approximately as
$E^{-1.5}$. We present a new model of particle acceleration in systems with a
bath of merging magnetic islands that self-consistently describes the
development of velocity-space anisotropy parallel and perpendicular to the
local magnetic field and includes the self-consistent feedback of pressure
anisotropy on the merging dynamics. By including pitch-angle scattering we
obtain an equation for the omni-directional particle distribution $f(v,t)$ that
is solved in closed form to reveal $v^{-5}$ (corresponding to an energy flux
varying as $E^{-1.5}$) as a near-universal solution as long as the
characteristic acceleration time is short compared with the characteristic loss
time. In such a state the total energy in the energetic particles reaches
parity with the remaining magnetic free energy. More generally, the resulting
transport equation can serve as the basis for calculating the distribution of
energetic particles resulting from reconnection in large-scale inhomogeneous
systems.
