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The $T$-tour problem is a natural generalization of TSP and Path TSP. Given agraph $G=(V,E)$, edge cost $c: E \to \mathbb{R}_{\ge 0}$, and an evencardinality set $T\subseteq V$, we want to compute a minimum-cost $T$-joinconnecting all vertices of $G$ (and possibly containing parallel edges).  In this paper we give an $\frac{11}{7}$-approximation for the $T$-tourproblem and show that the integrality ratio of the standard LP relaxation is atmost $\frac{11}{7}$. Despite much progress for the special case Path TSP, forgeneral $T$-tours this is the first improvement on Seb\H{o}'s analysis of theBest-of-Many-Christofides algorithm (Seb\H{o} [2013]).

Improving on Best-of-Many-Christofides for $T$-tours