Let　[Formula　presented]　be　a　loopless　matroid　on　[Formula　presented]　with　rank　function　[Formula　presented].　Let　[Formula　presented]　and　[Formula　presented].　The　Matroid　Covering　and　Packing　Theorems　state　that　the　minimum　number　of　independent　sets　whose　union　is　[Formula　presented]　is　[Formula　presented],　and　the　maximum　number　of　disjoint　bases　is　[Formula　presented].　We　prove　refinements　of　these　theorems.　If　[Formula　presented],　where　[Formula　presented]　is　an　integer　and　[Formula　presented],　then　[Formula　presented]　can　be　partitioned　into　[Formula　presented]　independent　sets　with　one　of　size　at　most　[Formula　presented].　If　[Formula　presented],　then　[Formula　presented]　has　[Formula　presented]　disjoint　independent　sets　such　that　[Formula　presented]　are　bases　and　the　other　has　size　at　least　[Formula　presented].　We　apply　these　results　to　truncations　of　cycle　matroids　to　refine　graph-theoretic　results　due　to　Chen,　Koh,　and　Peng　in　1993　and　to　Chen　and　Lai　in　1996.　©　2018　Elsevier　Ltd