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We define 1 new type of resolvability called \( \alpha \)-pair-resolvability in which each point appears in each resolution class as a member of \( \alpha \)-pairs. The concept is intended for path designs (or other designs) in which the role of points in blocks is not uniform or for designs which are not balanced. We determine the necessary conditions and show they are sufficient for \( k = 3 \) and \( \alpha = 2,3 \) (\( \alpha \geq 2 \) is necessary in every case). We also consider near \( a \)-pair-resolvability and show the necessary conditions are sufficient for \( \alpha = 2,4 \). We consider under what conditions it is possible for the ordered blocks of a path design to be considered as unordered blocks and thereby create a triple system (a tight embedding) and there also we show the necessary conditions are sufficient. We show it is always possible to embed maximally unbalanced path designs \( \text{PATH}(v, 3, 1) \) into \( \text{PATH}(v + s, 3, 1) \) for admissible \( s \), and to embed any \( \text{PATH}(v, 3, 2\lambda) \) into a \( \text{PATH}(v + s,3, 2\lambda) \) for any \( s \geq 1 \).