  It is known that any {\em real coordinate transformation} (RCT) to compress
waves in an unbounded domain into a bounded domain results in infinite
oscillations that cannot be resolved by any grid-based method. In this paper,
we intend to show that it is viable if the outgoing waves are compressed along
the radial direction and the resulting oscillatory pattern is extracted
explicitly. We therefore construct a perfectly matched layer (PML)-type
technique for domain reduction of wave scattering problems using RCT, termed as
real compressed layer (RCL). Different from all existing approaches, the RCL
technique has two features: (i) the RCL-equation only involves real-valued
coefficients, which is more desirable for computation and analysis; and (ii)
the layer is not ``artificial'' in the sense that the computed field in the
layer can recover the outgoing wave of the original scattering problem in the
unbounded domain. Here we demonstrate the essential idea and performance of the
RCL for the two-dimensional Helmholtz problem with a bounded scatterer, but
this technique can be extended to three dimensions in a similar setting.
