  Atoll sources are accreting neutron star (NS) low-mass X-ray binaries. We
present a spectral analysis of four persistent atoll sources (GX 3+1, 4U
1702$-$429, 4U 0614+091, and 4U 1746$-$371) observed for $\sim20$ ks each with
NuSTAR to determine the extent of the inner accretion disk. These sources range
from an apparent luminosity of $0.006-0.11$ of the Eddington limit (assuming
the empirical limit of $3.8\times10^{38}$ ergs s$^{-1}$). Broad Fe emission
features shaped by Doppler and relativistic effects close to the NS were firmly
detected in three of these sources. The position of the disk appears to be
close to the innermost stable circular orbit (ISCO) in each case. For GX 3+1,
we determine $R_{in}=1.8^{+0.2}_{-0.6}\ R_{\mathrm{ISCO}}$ (90% confidence
level) and an inclination of $27^{\circ}-31^{\circ}$. For 4U 1702$-$429, we
find a $R_{in}=1.5_{-0.4}^{+1.6}\ R_{\mathrm{ISCO}}$ and inclination of
$53^{\circ}-64^{\circ}$. For 4U 0614+091, the disk has a position of
$R_{in}=1.3_{-0.2}^{+5.4}\ R_{\mathrm{ISCO}}$ and inclination of
$50^{\circ}-62^{\circ}$. If the disk does not extend to the innermost stable
circular orbit, we can place conservative limits on the magnetic field strength
in these systems in the event that the disk is truncated at the Alfv\'{e}n
radius. This provides the limit at the poles of $B\leq6.7\times10^{8}$ G,
$3.3\times10^{8}$ G, and $14.5\times10^{8}$ G for GX 3+1, 4U 1702$-$429, and 4U
0614+091, respectively. For 4U 1746$-$371, we argue that the most plausible
explanation for the lack of reflection features is a combination of source
geometry and strong Comptonization. We place these sources among the larger
sample of NSs that have been observed with NuSTAR.
