  Several diffuse interstellar bands (DIBs) have profiles with resolved
sub-peaks that resemble rotational bands of large molecules. Analysis of these
profiles can constrain the sizes and geometries of the DIB carriers, especially
if the profiles exhibit clear variations along lines of sight probing different
physical conditions. Using the extensive data set from the EDIBLES survey we
searched for systematic variations in the peak-to-peak separation of these
sub-peaks for the $\lambda\lambda$5797, 6379, and 6614 DIBs in lines of sight
with a single dominant interstellar cloud. We used the spectra of twelve
single-cloud sight lines to measure the peak-to-peak separation in the band
profile substructures for these DIBs. We adopted the rotational contour
formalism to infer the rotational constant for each DIB carrier and the
rotational excitation temperature in the sight lines. We compared these to
rotational constants for linear and spherical molecules to estimate the DIB
carrier sizes. All three DIBs have peak separations that vary systematically
between lines of sight, indicating correlated changes in the rotational
excitation temperatures. We derived $B_{6614}$=$(22.2\pm8.9)\times 10^{-3}$
cm$^{-1}$, consistent with previous estimates. Assuming a similar rotational
temperature for the $\lambda$6614 DIB carrier and assuming a linear carrier, we
found B$_{5797}^{\rm linear}=(5.1\pm2.0)\times10^{-3}~{\rm cm}^{-1}$ and
B$_{6379}^{\rm linear} =(2.3\pm0.9)\times10^{-3}~{\rm cm}^{-1}$. If the
carriers of those DIBs however are spherical species, their rotational
constants are half that value, $B_{5797}^{\rm spherical} =
(2.6\pm1.0)\times10^{-3}~{\rm cm}^{-1}$ and $B_{6379}^{\rm spherical} =
(1.1\pm0.4)\times10^{-3}~{\rm cm}^{-1}$. We estimate molecule sizes that range
from 7--9 carbon atoms ($\lambda$6614 carrier, linear) to 77--114 carbon atoms
($\lambda$6379, spherical).
