Compounds generally have recessive accent, as φιλό-τι_μος loving-honor (τι_μή). But there are many exceptions, e.g.—
a. Primitives in -ά_, -ή, -ής, -εύς, -μός, and -έος usually keep their accent when compounded; except dissyllabic words in -ά_, -ή, -ής whose first part is not a preposition. Thus, κριτής
b. Compound adjectives in -ης, -ες are usually oxytone: εὐ-γενής
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].