Measurements of the dependence of the critical current I(c) on the ext
ernal magnetic field H in long Josephson junctions with a periodic lat
tice of inhomogeneities are presented. Commensurability between the la
ttice of inhomogeneities and the chain of fluxons induces equidistant
peaks in the I(c)(H)-curve. Some of these commensurability peaks are f
ound to be suppressed as predicted by the theory of Fehrenbacher et al
. which takes into account the finite width of the inhomogeneities. Th
e suppression of the I(c) peaks takes place when the width of each inh
omogeneity is equal to or a multiple of the spacing between the fluxon
s in the junction. Together with the suppression of the integer (harmo
nic) peaks predicted by theory, experimentally a suppression of subhar
monic peaks is also observed. A qualitative explanation of this new ef
fect is suggested.