A charge-carrier density dependent mobility has been predicted for amorphous, glassy energetically disordered semiconducting polymers, which would have considerable impact on their performance in devices. However, previous observations of a density dependent mobility are complicated by the polycrystalline materials studied. Here charge transport in field-effect transistors and diodes of two amorphous, glassy fluorene-triarylamine copolymers is investigated, and the results explored in terms of a charge-carrier density dependent mobility model. The nondispersive nature of the time-of-flight (TOF) transients and analysis of dark injection transient results and transistor transfer characteristics indicate a charge-carrier density independent mobility in both the low-density diode and the high-density transistor regimes. The mobility values for optimized transistors are in good agreement with the TOF values at the same field, and both have the same temperature dependency. The measured transistor mobility falls two to three orders of magnitude below that predicted from the charge-carrier density dependent model, and does not follow the expected power-law relationship. The experimental results for these two amorphous polymers are therefore consistent with a charge-carrier density independent mobility, and this is discussed in terms of polaron-dominated hopping and interchain correlated disorder.