Summary: Let \(S_n\), \(n \geq 1\), describe the successive sums of the payoffs in the classical St. Petersburg game. W. Feller’s famous weak law [Ann. Math. Stat. 16, 301–304 (1945; Zbl 0060.28701)] states that \(\frac{S_n}{n \log_2 n} \to 1\) in probability as \(n \to \infty\). However, almost sure convergence fails, more precisely, \(\limsup_{n \to \infty} \frac{S_n}{n \log_2 n} = + \infty\) a.s. and \(\liminf_{n \to \infty} \frac{S_n}{n \log_2 n} = 1\) a.s. as \(n \to \infty\). S. Csörgö and G. Simons [Stat. Probab. Lett. 26, No. 1, 65–73 (1996; Zbl 0859.60030)] have shown that almost sure convergence holds for trimmed sums, that is, for \(S_n - \max_{1 \leq k \leq n} X_k\) and, moreover, that this remains true if the sums are trimmed by an arbitrary fixed number of maximal sums. A predecessor of the present paper was devoted to sums trimmed by the random number of maximal summands. The present paper concerns analogues for the random number of summands equal to the minimum, as well as analogues for joint trimmings.