Context. 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. Aims. Using the extensive data set from the ESO Diffuse Interstellar Bands Large Exploration Survey (EDIBLES) we searched for systematic variations in the

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... o-peak separation of these sub-peaks for three well-known DIBs in lines of sight with a single dominant interstellar cloud. Methods. We used the spectra of twelve single-cloud sight lines to examine the λλ5797, 6379, and 6614 DIB profiles. We measured the peak-to-peak separation in the band profile substructures for these DIBs. We adopted the rotational contour formalism for linear or spherical top molecules to infer the rotational constant for each DIB carrier and the rotational excitation temperature in the sight lines. We compared these to experimentally or theoretically obtained rotational constants for linear and spherical molecules to estimate the DIB carrier sizes. Results. All three DIBs have peak separations that vary systematically between lines of sight, indicating correlated changes in the rotational excitation temperatures. The rotational constant B of the λ6614 DIB was determined independently of the rotational excitation temperature; we derived B 6614 =(22.2 ± 8.9) × 10 −3 cm −1 , consistent with previous estimates. Assuming a similar rotational temperature for the λ6614 DIB carrier and assuming a linear carrier, we found B linear 5797 = (5.1 ± 2.0) × 10 −3 cm −1 and B linear 6379 = (2.3 ± 0.9) × 10 −3 cm −1 . If the carriers of those DIBs are spherical species, on the other hand, their rotational constants are half that value, B spherical 5797 Conclusions. Systematic variations in the DIB profiles provide the means to constrain the molecular properties. We estimate molecule sizes that range from 7-9 carbon atoms (λ6614 carrier, linear) to 77-114 carbon atoms (λ6379, spherical).