  The "similarity" degree of a unital operator algebra $A$ was defined and
studied in two recent papers of ours, where in particular we showed that it
coincides with the "length" of an operator algebra. This paper brings several
complements: we give direct proofs (with slight improvements) of several known
facts on the length which were only known via the degree, and we show that the
length of a type $II_1$ factor with property $\Gamma$ is at most 5, improving
on a previous bound ($\le 44$) due to E. Christensen.
