The amalgam of L p and ℓ q consists of those functions for which the sequence of L p -norms over the intervals [ n , n + 1 ) is in ℓ q . These spaces ( L p , ℓ q ) have been studied in several recent papers. Here we replace the intervals [ n , n + 1 ) by a cover α = { I n ; n ∈ Z } of the real line consisting of disjoint half-open intervals I n each of the form [ a , b ) , and investigate which properties of ( L p , ℓ q ) carry over to these irregular amalgams ( L p , ℓ q ) α . In particular, we study how ( L p , ℓ q ) α varies as p , q , and α vary and determine conditions under which translation is continuous.