The transient-current technique (TCT) with the laser beam directed at the detector edge (known as Edge-TCT or E-TCT) is a powerful method for investigating the properties of irradiated strip detectors. In the studies published so far a narrow infra-red (IR) laser beam was directed at the detector perpendicular to the direction of the strips. IR light (λ = 1064 nm) has a long penetration depth in silicon and so the carriers are released below several consecutive strips. The carriers drifting to the strips in the vicinity of the readout strip contribute to the induced transient current. In this work Edge-TCT measurements with a laser beam directed parallel to the strips are investigated. It is shown that this modality should be used to measure the charge-collection profiles of irradiated strip detectors because E-TCT with light injection perpendicular to the strips overestimates the contribution to the collected charge from the rear side of the detector.