ABSTRACT We present an analysis of major-axis surface-brightness profiles of bars in a volume-limited sample of 182 barred spiral galaxies, using Spitzer 3.6 $\mu$m images. Unlike most previous studies, we use the entire bar profile, and we classify profiles into four categories. These are ‘Peak+Shoulders’ (P+Sh) – updating the classic ‘flat bar’ profile – and three subtypes of the classic ‘exponential’ profile: (true) Exponential, ‘Two-Slope’ (shallow inner slope + steeper outer slope), and ‘Flat-Top’ (constant inner region, steep outer slope). P+Sh profiles are preferentially found in galaxies with high stellar masses, early Hubble types, red colours, and low gas fractions; the most significant factor is stellar mass, and previous correlations with Hubble type can be explained by the tendency of higher-mass galaxies to have earlier Hubble types. The most common type of non-P+Sh profile is Exponential, followed by Flat-Top profiles; all non-P+Sh profiles appear to have similar distributions of stellar mass, Hubble type, colour, and gas fraction. We also morphologically classify the bars of an inclined subsample into those with and without boxy/peanut-shaped (B/P) bulges; as previously reported, the presence of a B/P bulge is very strong function of stellar mass. Essentially all bars with B/P bulges have P+Sh profiles; we associate the profile shoulders with the outer, vertically thin part of the bar. We find a small number of P+Sh profiles in bars without clear B/P bulges, which may indicate that P+Sh formation precedes the formation of B/P bulges.