We report the results of two simple studies that seek observational evidence that solar coronal loops are unstable to the MHD kink instability above a certain critical value of the total twist. First, we have used Yohkoh soft X-ray telescope image sequences to measure the shapes of 191 X-ray sigmoids and to determine the histories of eruption (evidenced by cusp and arcade signatures) of their associated active regions. We find that the distribution of sigmoid shapes is quite narrow and the frequency of eruption does not depend significantly on shape. Second, we have used Mees Solar Observatory vector magnetograms to estimate the large-scale total twist of active regions in which flare-related signatures of eruption are observed. We find no evidence of eruption for values of large-scale total twist remotely approaching the threshold for the kink instability.