This work reports on nine new bands of the CCH B∼ 2A′←X̃ 2∑+ system recorded by laser-induced fluorescence. In addition, the 37 946 and 38 107 cm-1 bands were revisited in a supersonic molecular beam. Of these 11 bands, ten were in the 36 600-39 700 cm-1 range; they were rotationally analyzed and assigned as transitions from low vibronic levels, X̃(0,υ2,υ3) (υ2=2-4 and υ3 = 0-1) of CCH to two vibrational levels (T,T+1221) of the B̃ state. Although previously observed as too weak, these bands were enhanced in this work by relaxing vibrationally excited CCH with SF6, instead of He or Ar. The rotationally resolved 35 939 cm-1 band, the band outside of the range of 36600-39700 cm-1, is assigned as B̃(T+775)←X̃(0,91,0). These new bands, together with transitions previously reported, are simultaneously analyzed in a nonlinear fit. This work obtained the first spectroscopic parameters of X̃(0,20,0), X̃(0,22,0), X̃(0,22,1), B̃(T+775), and B̃(T+1221), and further improved the spectroscopic parameters of X̃(0,31,0), X̃(0,33,0), and B̃(T). Though the rotational constants of the B state have a very small vibrational dependence, their spin-rotation constants increase by a factor of 2 within 1221 cm-1, suggesting that the B̃ state is perturbed by the nearby unobserved C̃2A″ state via the Renner-Teller effect.