if you cannot get suitable dates LHR-DXB-HEL-LHR, try LHR-HEL-DXB-LHR
LX have flights ZRH-DXB-ZRH. When LX join Oneworld this will be another DXB mileage earning opportunity
LHR-DXB 3420 miles
HEL-DXB 2819
ZRH-DXB 2966
Other milage runs in EU
LHR-IST 1565 (BA)
ZRH-JED 2461 (LX)
ZRH-MCT 3178 (LX)
LHR-MCT 3624 (BA)
HEL-LPA 2921 (AY may be seasonable)
HEL-TFS 2626 (AY may be seasonable)
HEL-FNC 2678 (AY may be seasonable)
To use the 20th segement could go SFO-ORD-LAX-DFW-ORD-LAX (7372 miles) instead of SFO-ORD-LAX-ORD-LAX. I guess there are plenty of other places which could become the 20th segment and still get you to ORD LAX when you want.
[This message has been edited by Mwenenzi (edited Dec 06, 2003).]