  A new inversion method for determining near-surface shear currents from a
measured wave spectrum is introduced. The method is straightforward to
implement and starts from the existing state-of-the-art technique of assigning
effective depths to measured wavenumber-dependent Doppler shift velocities. A
polynomial fit is performed, with the coefficients scaled based on a simple
derived relation to produce a current profile that is an improved estimate of
the true profile. The method involves no user-input parameters, with the
optimal parameters involved in the polynomial fit being chosen based on a
simple criterion involving the measured Doppler shift data only. The method is
tested on experimental data obtained from a laboratory where current profiles
of variable depth dependence could be created and measured by particle image
velocimetry, which served as "truth" measurements. Applying the new inversion
method to experimentally measured Doppler shifts resulted in a $>3\times$
improvement in accuracy relative to the state-of-the-art for current profiles
with significant near-surface curvature. The experiments are dynamically
similar to typical oceanographic flows such as wind-drift profiles and our
laboratory thus makes a suitable and eminently useful scale model of the
real-life setting. Our results show that the new method can achieve improved
accuracy in reconstructing near-surface shear profiles from wave measurements
by a simple extension of methods which are currently in use, incurring little
extra complexity and effort. A novel adaptation of the normalized scalar
product method has been implemented, able to extract Doppler shift velocities
as a function of wavenumber from the measured wave spectrum.
