We measure the viscoelastic properties of a highly entangled narrow molecular weight polyisoprene melt with approximately 280 entanglements per chain in steady and transient shear and in elongational flows. The storage and loss moduli of the melt are found to be well described by the Milner and McLeish model. The relaxation modulus G(t, gamma) is measured using stress relaxation after a sudden shearing displacement and we experimentally determine the Rouse time tau R by observing strain-time separability G(t, gamma) = G (t) h(gamma) for t > tau R. The transient elongational properties are measured using three distinct instruments: the Sentmanat extensional rheometer (SER) universal testing platform from Xpansion Instruments, its counterpart, the extensional viscosity fixture (EVF) from TA Instruments, and a filament stretching rheometer (FSR). The kinematics obtained in each device is sensitive to the aspect ratio of the sample and care must be taken to achieve homogeneous deformation conditions. Especially for the SER and EVF instruments, a second aspect ratio associated with the rectangular cross-section of the sample is also important. We find that the initial growth in the tensile stress follows the prediction given by the Doi-Edwards reptation model for Deborah numbers based on the Rouse time less than about De(R)=0.04. For De(R)=0.04, the stress difference follows more or less the Doi-Edwards prediction in the limit of infinite stretch rates and, for De(R) > 0.04, the measured stresses are well above those that can be predicted by the basic Doi-Edwards model. When De(R) > 1, the stress difference also exceeds the linear viscoelastic prediction. In conjunction with this strain-hardening response, a stabilization is obtained whereby the limiting Hencky strain before sample rupture is markedly increased. We compare our observations in the regime 0.04 < De(R) < 1 with available experiments and theories. The stabilization for De(R) > 1 is interpreted as a signature of chain stretching for elongational deformation rates faster than the inverse Rouse time. (C) 2009 The Society of Rheology. [DOI: 10.1122/1.3208073]