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Let      A A       be a finite dimensional tame algebra over an algebraically closed field      k k      . It has been conjectured that any almost split sequence      0 →  X →  ⊕  i = 1 n Y i →  Z →  0 0 \to X \to \oplus _{i=1} ^n Y_i \to Z \to 0       with      Y i Y_i       indecomposable modules has      n ≤  5 n \le 5       and in case      n = 5 n=5      , then exactly one of the      Y i Y_i       is a projective-injective module. In this work we show this conjecture in case all the      Y i Y_i       are directing modules, that is, there are no cycles of non-zero, non-iso maps      Y i = M 1 →  M 2 →  ⋯  →  M s = Y i Y_i =M_1 \to M_2 \to \cdots \to M_s=Y_i       between indecomposable      A A      -modules. In case,      Y 1 Y_1       and      Y 2 Y_2       are isomorphic, we show that      n ≤  3 n \le 3       and give precise information on the structure of      A A      .

On the number of terms in the middle of almost split sequences over tame algebras