Uncle Phil
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Yep, I ran up Stelvio (and all over the Alps) on a ST1300 rental.You can certainly tour on a ST1300 in the Alps, but it is easier to "sport" tour on one of the lighter alternatives.
Stelvio was especially 'interesting' since this particular ST1300 suffered from 'notchy throttle'.
And I've run Hard Knott Pass in the UK on a ST1300 - which can also be a bit 'challenging' - up the 'fort' side.
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But I'm used to the ST1100s in all sorts of conditions so the ST1300 was not a big deal for me.