VECM - a weird case

[loooooo]

Hi,

I've got three I(1) series, each of which is reported to have a unit root with no drift nor trend.
Nevertheless, Johansen's testing procedure (both trace and max-eigenvalue tests) indicates 3 cointegrating relations when specified with a drift in CE and 2 without it.
I know it can hardly be the case that there are 3 cointegrating relations for 3 I(1) series, so it looks like I should go for 2 CEs with no drift, but not 100% sure here.
Does anyone have any idea what the cause may be and what sort of judgement should be made as for this?
I need your help, econometricians!

Thanks,