  Reports of weak local minima in the magnetoresistance at $\nu=2+3/5$,
$2+3/7$, $2+4/9$, $2+5/9$, $2+5/7$, and $2+5/8$ in the second Landau level of
the electron gas in GaAs/AlGaAs left open the possibility of fractional quantum
Hall states at these filling factors. In a high quality sample we found that
the magnetoresistance exhibits peculiar features near these filling factors of
interest. These features, however, cannot be associated with fractional quantum
Hall states; instead they originate from magnetoresistive fingerprints of the
electronic bubble phases. We found only two exceptions: at $\nu=2+2/7$ and
$2+5/7$ there is evidence for incipient fractional quantum Hall states at
intermediate temperatures. As the temperature is lowered, these fractional
quantum Hall states collapse due to a phase competition with bubble phases.
