The bassoon has side holes a few tens of millimeters long, much longer than in other woodwinds. When they are closed, the ``quarter-wave" resonances of these ``chimneys" create short circuits in parallel with the bore. At these resonance frequencies, near 2~kHz --within the sensitive range of hearing-- it is expected that the waves will not propagate beyond the chimney, affecting both the input impedance and the radiated sound. Using parametric studies with varying chimney lengths, these effects on impedance and radiated sound are measured for a French bassoon and a simplified conical model instrument. The effects are clear on the model instrument, especially when several chimneys have equal length. For the bassoon, the passive filter effect remains, but its importance on the sound is blurred due to changes in the oscillation regime and in the directivity, as simulations confirmed. The effect is audible under laboratory conditions, but in the same order of magnitude as the spatial level variations due to the directivity. It is therefore unlikely that the difference in timbre between the French and the German bassoon is mainly due to longer tone hole chimneys.