  The properties of compact binaries, such as masses and spins, are imprinted
in the gravitational-waves they emit and can be measured using parameterised
waveform models. Accurately and efficiently describing the complicated
precessional dynamics of the various angular momenta of the system in these
waveform models is the object of active investigation. One of the key models
extensively used in the analysis of LIGO and Virgo data is the
single-precessing-spin waveform model IMRPhenomPv2. In this article we present
a new model IMRPhenomPv3 which includes the effects of two independent spins in
the precession dynamics. Whereas IMRPhenomPv2 utilizes a single-spin
frequency-dependent post-Newtonian rotation to describe precession effects, the
improved model, IMRPhenomPv3, employs a double-spin rotation that is based on
recent developments in the description of precessional dynamics. Besides
double-spin precession, the improved model benefits from a more accurate
description of precessional effects. We validate our new model against a large
set of precessing numerical-relativity simulations. We find that IMRPhenomPv3
has better agreement with the inspiral portion of precessing binary-black-hole
simulations and is more robust across a larger region of the parameter space
than IMRPhenomPv2. As a first application we analyse, for the first time, the
gravitational-wave event GW151226 with a waveform model that describes two-spin
precession. Within statistical uncertainty our results are consistent with
published results. IMRPhenomPv3 will allow studies of the measurability of
individual spins of binary black holes using GWs and can be used as a
foundation upon which to build further improvements, such as modeling
precession through merger, extending to higher multipoles, and including tidal
effects.
