diff --git a/libsmallrna/libsmallrna/libsmallrna.pyx b/libsmallrna/libsmallrna/libsmallrna.pyx
index 62a6caef6b0a13964d0d32f2f08f889e66dc8ff0..b0326e0357bf73c0a730743e0a2d8a68c8ff4c55 100755
--- a/libsmallrna/libsmallrna/libsmallrna.pyx
+++ b/libsmallrna/libsmallrna/libsmallrna.pyx
@@ -355,8 +355,13 @@ def count_sis(annot_infos, write_queue):
         # Eliminate most common non-siRNA target cases based on annotation name.
         # Also eliminate the reads with no signature
         # (the annot_name should be "no_signature")
-        if (annot_name in COMMON_NO_TARGET
-            or annot_name[:3] == "no_"):
+        # if (annot_name in COMMON_NO_TARGET
+        #     or annot_name[:3] == "no_"):
+        #     continue
+        # Actually, we do accept reads that do not start with G
+        # Provided they are not plain "no_signature"
+        # (that is: without other annotations) 
+        if annot_name in COMMON_NO_TARGET:
             continue
         # annotations: set of tuples
         # (attrs["gene_biotype"], gtf.strand, gtf.start, gtf.end, attrs["gene_id"])