Legman, in Randolph-Legman, "Roll Me in Your Arms," had this to say about Brady (p. 470, in 151. Peggy Howatt):
"A similar trait exists in another 1910s topical ballad, not bawdy, entitled "Brady" (in Hiler's "Full Dress Suits and Plenty of Whores, manuscript, Paris, 1928), in which the policeman and the badman in East St. Louis, Illinois, both shoot each other simultaneously. And the song ends with the delicate doubt expressed- in what has to be one of the greatest rhymes in the English language!- as to whether either of them will arrive in heaven at all, or perhaps have gone elsewhere, when St. Peter reacts impatiently, after waiting for them far too long:

St. Peter standing by the gate
Says, Ain't them fellows kind o' late?
Seems to me that's mighty curious,
Two hot sports from East St. Lourious.

Too bad that this manuscript has not been published.