I have run regular rather than premium in all my BMW's for the past 15 years or so. BMW's are only mildly high compression engines and they easily handle the adjustment to lower octane fuel. I've tested fuel mileage a bit (not extensively), and I found no detectable impairment to my mpg.

If you were "tracking" the car or otherwise driving it hard, I could see feeding it higher octane fuel, but I drive fairly conservatively and see no benefit to it.

My son once had a Toyota with the 2ZZGE engine by Yamaha. THAT one did get premium, but its compression ratio was quite a bit higher than these BMW engines.

AM.

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E70 2010 3.0 M57 AT Titanium Silver with Black Leather
E53 2004 3.0 M54 AT Toledo Blue with Gray Leather
E83 2008 3.0 N52 AT Silver Gray Metallic with Black Vinyl
E46 1999 2.8 M52TU 5MT Black with Tan Leather 250K+ miles (Sold, but not forgotten)