Let c [les ] 0.076122 and T1, T2,…, Tn be a sequence of trees such that [mid ]V(Ti)[mid ] [les ] i−c(i−1). We prove that, if for each 1 [les ] i [les ] n there exists a vertex xi ∈ V(Ti) such that Ti−xi has at least (1−2c)(i−1) isolated vertices, then T1,…, Tn can be packed into Kn. We also prove that if T is a tree of order n+1−c′n, c′ [les ] 1/25 (37−8 √21 ) ≈ 0.0135748, such that there exists a vertex x ∈ V(T) and T−x has at least n(1−2c′) isolated vertices, then 2n+1 copies of T may be packed into K2n+1.