  As the most extreme members of the rapidly evolving faint blue galaxy
population at intermediate redshift, the compact narrow emission line galaxies
(CNELGs) are intrinsically luminous (-22 < M_B < -18) with narrow emission
linewidths (30 < \sigma < 125 km/s). Their nature is heavily debated: they may
be low-mass starbursting galaxies that will fade to present-day dwarf galaxies
or bursts of star formation temporarily dominating the flux of more massive
galaxies, possibly related to in situ bulge formation or the formation of cores
of galaxies. We present deep, high-quality (~0.6 - 0.8 arcsec) images with CFHT
of 27 CNELGs. One galaxy shows clear evidence for a tidal tail; the others are
not unambiguously embedded in galactic disks. Approximately 55% of the CNELGS
have sizes consistent with local dwarfs of small-to-intermediate sizes, while
45% have sizes consistent with large dwarfs or disks galaxies. At least 4
CNELGs cannot harbor substantial underlying disk material; they are
low-luminosity galaxies at the present epoch (M_B > -18). Conversely, 15 are
not blue enough to fade to low-luminosity dwarfs (M_B > -15.2). The majority of
the CNELGs are consistent with progenitors of intermediate-luminosity dwarfs
and low-luminosity spiral galaxies with small disks. CNELGs are a heterogeneous
progenitor population with significant fractions (up to 44%) capable of fading
into today's faint dwarfs (M_B > -15.2), while 15 to 85% may only experience an
apparently extremely compact CNELG phase at intermediate redshift but remain
more luminous galaxies at the present epoch.
