Context. Pluto has five known satellites with diameters ranging from ∼1200 km down to ∼40 km, a possible outcome of a collisional origin. Smaller objects probably exist and may maintain tenuous rings, thus representing hazards during the New Horizons flyby of July 2015. Aims. The goal is to provide an upper limit for the numbers of unseen small bodies and/or equivalent widths of putative Pluto rings. Methods. We use a Pluto stellar appulse on April 10, 2006, and a stellar occultation by the dwarf planet on June 14, 2007, to scan Pluto's surroundings. Results. Our best data set places a 3σ upper limit of 0.3 km for the radius of isolated moonlets that we can detect. In the absence of detection, we derive an upper limit of 15 000 for the number of such bodies at distances smaller than ∼70 000 km from Pluto's system barycenter. We place a 3σ upper limit of typically 30−100 m for the equivalent width of ring material at barycentric distances ranging from 13 000 to 70 000 km. This limit applies for narrow rings only, i.e. less than about 10 km in width.