We report improvements in the quality of two-dimensional (2D) electrons in modulation-doped AlAs quantum wells, leading to electron mobilities as high as 31 m(2)/Vs, a ten-fold increase over the mobility of previous AlAs samples. Confirming the quality of our quantum wells, developing fractional quantum Hall states are observed in the first Landau level at high order filling factors nu=2/5, 3/5, 3/7, 4/7, and 4/9, and at larger fillings, at nu=4/3, 5/3, 7/3, 8/3, 8/5, and 11/3. Thanks to the much larger effective mass and g factor of AlAs 2D electrons compared to GaAs, and to the possible multivalley occupancy of AlAs 2D electrons, our improved systems help bring a wider scope to the investigation of low-disorder, interacting 2D electrons. (C) 2002 American Institute of Physics.