Eighty-one microwave resonances in Na Rydberg states n =21-35 between d, f, g, and h states have been accurately measured. Among them 43 transitions are first-time measurements, and 38 transitions have been improved, primarily by the elimination of stray electric and magnetic fields, compared with previous measurements.For the d ftra-nsitions, the measured intervals and d-state fine-structure splittings are a factor of 10 more precise; for d-g and d-h series, the measured intervals are a factor of 3 more precise than before. The n f-state fine-structure splittings in Na for n =21-29 have also been accurately measured, and the conclusion that the Na f-state fine-structure splitting n f5/ 2 n f7/ 5 is about 5% smaller than the hydrogen f-state fine-structure interval is confirmed through n =29. PACS number(s): 32.30.Bv, 32.80.Rm, 32.60.+i, 35.80.+s