  We describe a new, non-parametric, method for reconstructing lensing mass
distributions in multiple-image systems, and apply it to PG1115, for which time
delays have recently been measured. It turns out that the image positions and
the ratio of time delays between different pairs of images constrain the mass
distribution in a linear fashion. Since observational errors on image positions
and time delay ratios are constantly improving, we use these data as a rigid
constraint in our modelling. In addition, we require the projected mass
distributions to be inversion-symmetric and to have inward-pointing density
gradients. With these realistic yet non-restrictive conditions it is very easy
to produce mass distributions that fit the data precisely. We then present
models, for $H_0=42$, 63 and 84 \kmsmpc, that in each case minimize
mass-to-light variations while strictly obeying the lensing constraints. (Only
a very rough light distribution is available at present.) All three values of
$H_0$ are consistent with the lensing data, but require quite different
morphologies for the lensing galaxy. If $H_0$ is low, the main lensing galaxy
could be an early type. If $H_0$ is high, the galaxy is reconstructed as a late
elliptical or nearly edge-on disc; a binary or merging system is also
plausible.
