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tokens: to distance determinations made with the Baade-Wesselink method, and bias the calibration of the IR period–luminosity relation. Our previous works ( Mérand et al. 2006 ; Gallenne et al. 2011 , 2013 ) showed that these CSEs have an angular size of a few stellar radii and a flux contribution to the photosphere ranging from 2% to 30%. While in the near-IR the CSE emission might be negligible compared with the stellar continuum, this is not the case in the mid- and far-IR, where the CSE emission dominates. Mérand et al. (2007) and Gallenne et al. (2011 , 2013) pointed out a possible correlation between the pulsation period and the CSE brightness in the near- and mid-IR. It seems that long-period Cepheids have brighter CSE than shorter period Cepheids. This could indicate a mass-loss mechanism linked to the stellar pulsation, and therefore that heavier stars experience higher mass-loss rate. This also seems to be consistent with the theoretical work of Neilson Lester (2008) who found a correlation between the mass-loss rate and the pulsation period. As discussed in Sect. 3 , our SPIPS fits from to band provide estimates of IR excess at m and m for Cepheids having Spitzer light curves ( Scowcroft et al. 2011 ). The derived excess magnitudes are listed in Table 2 . Examples of our final fit are shown in Figs. A.1 , A.2 , and A.4 . We clearly see an offset above the photospheric level (in grey), and the stars appear brighter due to the presence of IR excess. In Fig. 7 we plotted those IR excess with respect to the pulsation period, and we note that all stars exhibit an excess. However, the trend seems constant with the period at these wavelengths, which differs from our previous studies at 2.2 and m for Galactic Cepheids. We performed a linear and constant fit for both wavelengths combining all Magellanic Cloud Cepheids. From an -test, we found that a constant model is more statistically significant. We estimated an average excess of mag and mag (again, we took the standard deviation). These excesses are particularly significant and might be the signature of circumstellar dust. These results are relevant for the mid-IR calibration of the Cepheid distance scale (see e.g. Freedman et al. 2012 ). Some authors find that there are several advantages to using a mid-infrared relation. The effect of the dust extinction is reduced, the intrinsic dispersion is smaller than in the band, and the metallicity effect is supposed to be minimal. However, going to longer wavelengths brings new systematics that impact the distance scale, and which are usually not taken into account. Our measured IR excesses convert to a systematic error of 2.6% and 3% on the distance at 3.6 and m, respectively. Unfortunately, recent papers ( Scowcroft et al. 2016 ; Freedman et al. 2012 ; Monson et al. 2012 ) do not take into account this additional uncertainty. On the other hand, their relation is calibrated for a Cepheid plus a CSE, which is still valid if we assume that all Cepheids