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We have explored morphology of DNA molecules bound with Cu complexes of piroxicam (a non-steroidal anti-inflammatory drug) molecules under one-dimensional confinement of thin films and have studied the effect of counterions present in a buffer. X-ray reflectivity at and away from the Cu K absorption edge and atomic force microscopy studies reveal that confinement segregates the drug molecules preferentially in a top layer of the DNA film, and counterions enhance this segregation.