> in other words, all but the first row of a group.

Interesting question. The below should work and be quick so long as
there is a UNIQUE(col1, col2) constraint.

SELECT col1
     , col2
  FROM j
 WHERE col2 != (SELECT col2
                  FROM j AS jsub
                 WHERE col1 = j.col1
              ORDER BY col2 ASC
                 LIMIT 1);

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