  We present an investigation of the morphology and arrival times of integrated
radio pulses from the binary millisecond pulsar PSR J1022+1001. This pulsar is
renowned for its poor timing properties, which have been postulated to
originate from variability in its average pulse profile. Although a sub-class
of long-period pulsars are known to exhibit mode changes that give rise to very
large deviations in their integrated profiles, this was the first millisecond
pulsar thought to have an unstable mean profile. As part of a precision timing
program at the Parkes radio telescope we observed this pulsar between January
2003 and March 2004 using a coherent de-dispersion system (CPSR2). A study of
morphological variability during our brightest observations suggests that the
pulse profile varies by at most a few percent, similar to the uncertainty in
our calibration. Unlike previous authors, we find that this pulsar times
extremely well. In five minute integrations of 64 MHz bands we obtain a
weighted RMS residual of just 2.27 microseconds. The reduced chi-squared of our
best fit is 1.43, which suggests that this pulsar can be timed to high accuracy
with standard cross-correlation techniques. Combining relativistic constraints
with the pulsar mass function and consideration of the Chandrasekhar mass limit
on the white dwarf companion, we can constrain the inclination angle of the
system to lie within the range 37 < i < 56 degrees. For reasonable pulsar
masses, this suggests that the white dwarf is at least 0.9 solar masses. We
also find evidence for secular evolution of the projected semi-major axis.
