  We demonstrate that hybrid laser wakefield and direct acceleration (LWDA) can
be significantly improved by using two laser pulses with different
polarizations or frequencies. The improvement entails higher energy and charge
of the accelerated electrons, as well as weaker sensitivity to the time delay
between the leading (pump) pulse responsible for generating the wakefield, and
the trailing laser pulse responsible for direct laser acceleration (DLA). When
the two laser pulses have the same frequency, it is shown that it is
advantageous to have their polarization states orthogonal to each other. A
specific scenario of a frequency-doubled ($\lambda_{\rm DLA}=\lambda_{\rm
pump}/2$) DLA laser pulse is also considered, and found to be an improvement
over the single-frequency ($\lambda_{\rm DLA} = \lambda_{\rm pump}$) scenario.
