There is some theoretical evidence that full Bose–Einstein condensation (BEC) is achieved at the free surface of superfluid 4He where the density is small. We present new variational results of the BEC and of the density fluctuation spectrum in the surface region of a slab of 4He. We use both a standard wave function (wf) with bulk correlations and one body shape terms and a novel shadow wave function with a glue term (G-SWF). This last one describes the self- binding of 4 He only via interparticle correlations. In both cases we find that BEC increases from the bulk like value well inside the slab to a much larger value in the surface region but a striking different behavior is found in the low density region. With a standard wf the BEC reaches essentially 100% in the surface region. With the G-SWF the condensate only increases up to about 51%. Further out of the surface the condensate decreases and correspondingly there is an enhanced population of small momentum states. This different behavior is correlated with the presence in the G-SWF of enhanced density fluctuations in the surface region due to the zero point motion of ripplons. This enhancement is absent in the case of a standard wf.