diff --git a/qpms/cybspec.pyx b/qpms/cybspec.pyx
index 45cf286..7cbbc67 100644
--- a/qpms/cybspec.pyx
+++ b/qpms/cybspec.pyx
@@ -1,4 +1,5 @@
 import numpy as np
+cimport numpy as np
 import enum
 from .cycommon import get_mn_y, tlm2uvswfi
 __VSWF_norm_dict = {
@@ -140,6 +141,11 @@ cdef class BaseSpec:
         return self.__ilist[key]
 
     def __repr__(self):
+        cdef qpms_l_t lMax_candidate
+        lMax_candidate = qpms_nelem2lMax(len(self.__ilist) // 2)
+        if lMax_candidate >= 0:
+            if np.array_equal(self.__ilist, BaseSpec(lMax=lMax_candidate).ilist):
+                return 'BaseSpec(lMax=%d)' % lMax_candidate
         return 'BaseSpec([' + ','.join('%d' % i  for i in self.__ilist) + '])'
 
     property ilist:
diff --git a/qpms/indexing.h b/qpms/indexing.h
index e8ef012..11ac48e 100644
--- a/qpms/indexing.h
+++ b/qpms/indexing.h
@@ -63,6 +63,15 @@ static inline qpms_y_t qpms_lMax2nelem(qpms_l_t lmax){
 	return lmax * ((qpms_y_t)lmax + 2);
 }
 
+/// Inverse of qpms_lMax2nelem(); returns -1 if there is no exact match.
+static inline qpms_l_t qpms_nelem2lMax(qpms_y_t nelem) {
+  qpms_l_t l = qpms_y2n(nelem);
+  if (l == -qpms_yn2m(nelem, l))
+    return l - 1;
+  else
+    return -1;
+}
+
 // Scalar versions: they have a place for the 0, 0 term in the beginning
 
 /// Mapping from multipole degree, order to flat index (degree ≥ 0)