In this correspondence, the error exponents and decoding complexity of bina
ry woven convolutional codes with outer and inner warp are studied. It is s
hown that for both constructions an error probability that is exponentially
decreasing with the memory of the woven convolutional codes can be achieve
d with a nonexponentially increasing decoding complexity. Furthermore, the
error exponent for woven convolutional codes with inner warp is larger than
the one for woven convolutional codes with outer warp.