  Free-electron lasers (FELs) operate at wavelengths from millimeter waves
through hard x-rays. At x-ray wavelengths, FELs typically rely on
self-amplified spontaneous emission (SASE). Typical SASE emission contains
multiple temporal "spikes" which limit the longitudinal coherence of the
optical output; hence, alternate schemes that improve on the longitudinal
coherence of the SASE emission are of interest. In this paper, we consnider
electron bunches that are shorter than the SASE spike separation. In such
cases, the spontaneously generated radiation consists of a single optical pulse
with better longitudinal coherence than is found in typical SASE FELs. To
investigate this regime, we use two FEL simulation codes. One (MINERVA) uses
the slowly-varying envelope approximation(SVEA) which breaks down for extremely
short pulses. The second (PUFFIN) is a particle-in-cell (PiC) simulation code
that is considered to be a more complete model of the underlying physics and
which is able to simulate very short pulses. We first anchor these codes by
showing that there is substantial agreement between the codes in simulation of
the SPARC SASE FEL experiment at ENEA Frascati. We then compare the two codes
for simulations using electron bunch lengths that are shorter than the SASE
slice separation. The comparisons between the two codes for short bunch
simulations elucidate the limitations of the SVEA in this regime but indicate
that the SVEA can treat short bunches that are comparable to the cooperation
length.
