Hydrophobic polymers with low glass transition temperature (polyisoprenes) and a single head group (sulfonate) have been synthesized and characterized as insoluble monolayers on a water surface. The films are considerably thicker (10-50 nm) than conventional Langmuir monolayers of low molecular weight substances or polymers with surface-active repeating units. The thickness is inversely proportional to the area per head group. Films can be transferred via the Langmuir-Blodgett technique with transfer ratios close to 1. we use these monolayers as model systems to investigate the influence of the polymer chain statistics on the properties of solvent-free tethered polymers. We assume that each polymer chain is bound to the water phase with the head group and has the conformation of a distorted three-dimensional coil. The distortion increases with decreasing area per head group (A/n) and influences the isotherm of the polymer monolayers. We develop a theoretical description of this effect and conclude that, at a given area per head group, the surface pressure increases linearly with the chain length. In the case of Gaussian statistics, the slope of this line is proportional to the third power of the area per head group. In the case of non-Gaussian statistics, this slope can be expressed as a polynomial of Aln. The experimental data confirm these theoretical predictions. Deviations from Gaussian statistics can be neglected, and the description as a nonuniformly stretched brush (Semenov theory) comes closer to the experiment than the model of a uniformly stretched blush. Chains shorter than 300 repeat units systematically deviate from the theory.