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I'm not aware of a way to accomplish the task that you are asking about.
I would suggest a couple of things though:
1. build a crosstab below the viz that shows the exact values, use a highlight or filter action to show the number when a mark is hovered/selected.
2. Consider limiting the number of marks shown to the salient points. All the numbers in a viz are rarely referenced, it is likely that the max, min, or most recent marks are actually what you are shooting for.
3. Make the axis range smaller so that labels do not overlap.
Hope these suggestions help out.
Thanks for the quick reply, Nicholas. We're gearing up to use Tableau more interactively, but for the moment we're just creating static charts, so that's why we're fiddling with labels.
I'll look a little further into your suggestions. Thanks again!