diff --git a/frame/1m/packm/bli_packm_blk_var1.c b/frame/1m/packm/bli_packm_blk_var1.c
index 9ac9582db8..05263c4b7f 100644
--- a/frame/1m/packm/bli_packm_blk_var1.c
+++ b/frame/1m/packm/bli_packm_blk_var1.c
@@ -190,15 +190,16 @@ void bli_packm_blk_var1
 
 		inc_t  p_inc           = ps_p;
 
-		// NOTE: We MUST use round-robin partitioning when packing
-		// micropanels of a triangular matrix. Hermitian/symmetric
-		// and general packing may use slab or round-robin, depending
-		// on which was selected at configure-time.
-		// The definition of bli_packm_my_iter() will depend on whether slab
-		// or round-robin partitioning was requested at configure-time.
-		bool   my_iter         = bli_is_triangular( strucc )
-		    ? bli_packm_my_iter_rr( it, it_start, it_end, tid, nt )
-		    : bli_packm_my_iter   ( it, it_start, it_end, tid, nt );
+		// NOTE: We MUST use round-robin work allocation (bli_packm_my_iter_rr())
+		// when packing micropanels of a triangular matrix. Hermitian/symmetric
+		// and general packing may use slab or round-robin (bli_packm_my_iter()),
+		// depending on which was selected at configure-time.
+		bool my_iter = ( bli_is_triangular( strucc ) &&
+		                 bli_intersects_diag_n( diagoffc_i, panel_dim_i,
+		                                        panel_len_full )
+		                 ? bli_packm_my_iter_rr( it, it_start, it_end, tid, nt )
+		                 : bli_packm_my_iter   ( it, it_start, it_end, tid, nt )
+		               );
 
 		if ( bli_is_triangular( strucc ) &&
 		     bli_is_unstored_subpart_n( diagoffc_i, uploc, panel_dim_i, panel_len_full ) )