Context. Spectroscopic studies of ices in nearby star-forming regions indicate that ice mantles form on dust grains in two distinct steps, starting with polar ice formation (H2O rich) and switching to apolar ice (CO rich). Aims. We test how well the picture applies to more diffuse and quiescent clouds where the formation of the first layers of ice mantles can be witnessed. Methods. Medium-resolution near-infrared spectra are obtained toward background field stars behind the Pipe Nebula. Results. The water ice absorption is positively detected at 3.0 µm in seven lines of sight out of 21 sources for which observed spectra are successfully reduced. The peak optical depth of the water ice is significantly lower than those in Taurus with the same AV . The source with the highest water-ice optical depth shows CO ice absorption at 4.7 µm as well. The fractional abundance of CO ice with respect to water ice is 16+7 −6 %, and about half as much as the values typically seen in low-mass star-forming regions. Conclusions. A small fractional abundance of CO ice is consistent with some of the existing simulations. Observations of CO2 ice in the early diffuse phase of a cloud play a decisive role in understanding the switching mechanism between polar and apolar ice formation.@en