We present an analysis of measured current waveforms associated with positive and bipolar flashes recorded on the Säntis tower, Switzerland, from May 2010 till January 2012. The overall number of recorded flashes in the considered period was 201, of which 30 were of positive polarity (effectively transported positive charge to ground) and three were bipolar. The recorded positive flashes were mainly concentrated in the summer months, August being the month during which most of them occurred (6 events in 2010 and 16 events in 2011). The observed positive flashes are characterized by a median peak current of 11.8 kA, and a median flash duration of 80 ms. These values are consistent with those associated with the data recorded at the Gaisberg Tower in Austria. On the other hand, the amount of transferred charge is substantially larger in our dataset, with a median value of 169 C (6 times as large as the values obtained in Monte San Salvatore and in Japan, and 3 times as large as the value obtained in Austria). Eight flashes out of 30 transported positive charge to the ground in excess of 500 C. The obtained results confirm also the findings of Saba et al. according to which positive lightning flashes may combine high peak currents with high charge transfers (or flash durations). The three bipolar flashes recorded during the considered time period occurred during one storm occurred on August 27, 2011. The relative number of bipolar flashes (1.5%) is found to be lower than the values reported in previous studies in Austria and in Switzerland (3 to 6%). On the basis of the classification proposed by Rakov, two of the three observed bipolar flashes belonged to Type 2 and one to Type 3.