Get first and last record of a selection without using min() max()
as it turned out, it wasn't the MIN()/MAX() functions that slowed the query down, but the
WHERE DATE_FORMAT(strtime, '%Y-%m-%d') = CURDATE()

statement. Since the table has a column with the unix-timestap, using this instead accelerates it a lot:
WHERE TIMESTAMP &gt; UNIX_TIMESTAMP(CURDATE())

Query-time from ~3.6s down to ~0.02s. I call that a good improvement.