  In \cite{BCKM} it was shown that "Tiling implies Spectral" holds for a union
of three intervals and the reverse implication was studied under certain
restrictive hypotheses on the associated spectrum. In this paper, we
reinvestigate the "Spectral implies Tiling" part of Fuglede's conjecture for
the three interval case. We first show that the "Spectral implies Tiling" for
two intervals follows from the simple fact that two distinct circles have at
most two points of intersections. We then attempt this for the case of three
intervals and except for one situation are able to prove "Spectral implies
Tiling". Finally, for the exceptional case, we show a connection to a problem
of generalized Vandermonde varieties.
