Extreme ultraviolet spectra of highly charged tungsten ions were produced with an electron beam ion trap at the National Institute of Standards and Technology and recorded with a flat-field grazing-incidence spectrometer. The spectra were measured in the wavelength range 2.7-17.3 nm while the beam energy varied between 1.65 and 2.00 keV. At these energies, the ionization stages from Zr-like W34+ to Se-like W40+ ions were observed. Large-scale collisional-radiative modelling was used to identify the strong lines, including 15 new ones, which represent electric dipole n = 4-4 transitions in these ions. While a good quantitative agreement between theoretical and experimental data was found for almost all ions, some of the tentatively identified wavelengths in W35+ significantly disagree from all available calculations.