A dispenser for a roll of strip comprising a casing in which is disposed a roll of strip. Pivotally connected to the casing is a cover. At the strip exit opening is a passage through which advances the free end of the roll of strip. Disposed in the passage for the advancing free end of the roll of strip is an upwardly extending indexing member. The indexing member is formed with a curved tip and tapered side walls that are directed outwardly and downwardly. The roll of strip is formed with curved slits. The curved slits are alternately convex and concave. The indexing member penetrates each slit successively. The convex slit forms a convex opening upon entering the ticket exit passage which is penetrated by the indexing member. The convex slit forms a concave opening upon entering the ticket exit passage which is penetrated by the indexing member. The convex slit, when opened, forms a tongue contacting the penetrating tip of the indexing member. The concave slit, when opened, forms a pocket which is penetrated by the tip of the indexing member. An operator applying a downward force to the free end of the roll of strip severs the free end thereof successively along each successive slit by means of sharp edges at the base of the indexing member.