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.
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