Index: sys/kern/kern_cpuset.c
===================================================================
--- sys/kern/kern_cpuset.c
+++ sys/kern/kern_cpuset.c
@@ -1259,14 +1259,22 @@
 	if (set != NULL && rebase && nroot != tdroot) {
 		cpusetid_t base_id, root_id;
 
-		root_id = td->td_ucred->cr_prison->pr_cpuset->cs_id;
-		base_id = cpuset_getbase(td->td_cpuset)->cs_id;
-
-		if (base_id != root_id) {
-			error = cpuset_setproc_newbase(td, set, nroot, &base,
-			    &freelist, &domainlist);
-			if (error != 0)
-				goto unlock_out;
+		/*
+		 * For management purposes, we'll allow the system root to
+		 * entirely replace its cpuset with a jail's, as they may have
+		 * completely disjoint sets.
+		 */
+		error = priv_check(td, PRIV_JAIL_CPUSET);
+		if (error != 0) {
+			root_id = td->td_ucred->cr_prison->pr_cpuset->cs_id;
+			base_id = cpuset_getbase(td->td_cpuset)->cs_id;
+
+			if (base_id != root_id) {
+				error = cpuset_setproc_newbase(td, set, nroot,
+				    &base, &freelist, &domainlist);
+				if (error != 0)
+					goto unlock_out;
+			}
 		}
 	}
 
Index: sys/sys/priv.h
===================================================================
--- sys/sys/priv.h
+++ sys/sys/priv.h
@@ -136,6 +136,13 @@
 #define	PRIV_JAIL_SET		111	/* Set jail parameters. */
 #define	PRIV_JAIL_REMOVE	112	/* Remove a jail. */
 
+/*
+ * The default behavior is for jail attachment to augment the user's current
+ * cpuset, rather than replace it.  The system root is allowed to replace its
+ * cpuset entirely with a jail's when attaching to it, for management purposes.
+ */
+#define	PRIV_JAIL_CPUSET	113
+
 /*
  * Kernel environment privileges.
  */