  We present timing models for 20 millisecond pulsars in the Parkes Pulsar
Timing Array. The precision of the parameter measurements in these models has
been improved over earlier results by using longer data sets and modelling the
non-stationary noise. We describe a new noise modelling procedure and
demonstrate its effectiveness using simulated data. Our methodology includes
the addition of annual dispersion measure (DM) variations to the timing models
of some pulsars. We present the first significant parallax measurements for
PSRs J1024-0719, J1045-4509, J1600-3053, J1603-7202, and J1730-2304, as well as
the first significant measurements of some post-Keplerian orbital parameters in
six binary pulsars, caused by kinematic effects. Improved Shapiro delay
measurements have resulted in much improved pulsar mass measurements,
particularly for PSRs J0437-4715 and J1909-3744 with $M_p=1.44\pm0.07$
$M_\odot$ and $M_p=1.47\pm0.03$ $M_\odot$ respectively. The improved orbital
period-derivative measurement for PSR J0437-4715 results in a derived distance
measurement at the 0.16% level of precision, $D=156.79\pm0.25$ pc, one of the
most fractionally precise distance measurements of any star to date.
