diff --git a/src/grib_iterator_class_healpix.cc b/src/grib_iterator_class_healpix.cc
index 5f4fe2c18..8d8f06120 100644
--- a/src/grib_iterator_class_healpix.cc
+++ b/src/grib_iterator_class_healpix.cc
@@ -119,15 +119,15 @@ struct CodecFijNest
         return static_cast<int>(b);
     }
 
-    static std::tuple<int, int, int> nest_to_fij(int n, int k)
-    {
-        Assert(0 <= n);
-        auto f = n >> (2 * k);    // f = n / (Nside * Nside)
-        n &= (1 << (2 * k)) - 1;  // n = n % (Nside * Nside)
-        auto i = nest_decode_bits(n);
-        auto j = nest_decode_bits(n >> 1);
-        return { f, i, j };
-    }
+    // static std::tuple<int, int, int> nest_to_fij(int n, int k)
+    // {
+    //     Assert(0 <= n);
+    //     auto f = n >> (2 * k);    // f = n / (Nside * Nside)
+    //     n &= (1 << (2 * k)) - 1;  // n = n % (Nside * Nside)
+    //     auto i = nest_decode_bits(n);
+    //     auto j = nest_decode_bits(n >> 1);
+    //     return { f, i, j };
+    // }
 
     static int fij_to_nest(int f, int i, int j, int k)
     {
@@ -242,7 +242,11 @@ static int iterate_healpix(grib_iterator_healpix* self, long N)
     latitudes[2 * N - 1] = 0.0;
 
     if (self->nested) {
-        Assert(is_power_of_2(N));
+        if (!is_power_of_2(N)) {
+            grib_context* c = grib_context_get_default();
+            grib_context_log(c, GRIB_LOG_ERROR, "%s: For nested ordering, Nside must be a power of 2", ITER);
+            return GRIB_WRONG_GRID;
+        }
 
         const auto Nside = static_cast<int>(N);
         const auto k     = static_cast<int>(std::log2(Nside));
@@ -308,6 +312,7 @@ static int iterate_healpix(grib_iterator_healpix* self, long N)
         for (size_t i = 0, j=0; i < Ny; i++) {
             // Compute the longitudes at a given latitude
             for (double longitude : HEALPix_longitudes(N, i)) {
+                Assert( ring_to_nest.at(j) < Npix );
                 self->lons[ring_to_nest.at(j)] = longitude;
                 self->lats[ring_to_nest.at(j)] = latitudes[i];
                 ++j;
@@ -346,9 +351,7 @@ static int init(grib_iterator* iter, grib_handle* h, grib_arguments* args)
         return GRIB_WRONG_GRID;
     }
 
-    char ordering[32] = {
-        0,
-    };
+    char ordering[32] = {0,};
     size_t slen = sizeof(ordering);
     if ((err = grib_get_string_internal(h, sorder, ordering, &slen)) != GRIB_SUCCESS) {
         return err;
@@ -359,6 +362,10 @@ static int init(grib_iterator* iter, grib_handle* h, grib_arguments* args)
         grib_context_log(h->context, GRIB_LOG_ERROR, "%s: Only orderingConvention=(ring|nested) are supported", ITER);
         return GRIB_GEOCALCULUS_PROBLEM;
     }
+    if (self->nested && N == 1) {
+        grib_context_log(h->context, GRIB_LOG_ERROR, "%s: For orderingConvention=nested, N must be greater than 1", ITER);
+        return GRIB_GEOCALCULUS_PROBLEM;
+    }
 
     if (grib_is_earth_oblate(h) != 0) {
         grib_context_log(h->context, GRIB_LOG_ERROR, "%s: Only spherical earth is supported", ITER);
diff --git a/tests/grib_grid_healpix.sh b/tests/grib_grid_healpix.sh
index 59652e57b..96a719e28 100755
--- a/tests/grib_grid_healpix.sh
+++ b/tests/grib_grid_healpix.sh
@@ -72,6 +72,39 @@ EOF
 
 ${tools_dir}/grib_filter $tempFilt $tempGrib
 
+
+# Nested ordering
+# ---------------
+rm -f $tempGrib
+cat > $tempFilt <<EOF
+  set tablesVersion = $latest;
+  set gridType = "healpix";
+  set longitudeOfFirstGridPointInDegrees = 45;
+  set numberOfPointsAlongASide = 2;
+  set orderingConvention = "nested";
+  set values = { 0,1,2,3,4,5,6,7,
+    8,9,10,11,12,13,14,15,
+    16,17,18,19,20,21,22,23,
+    24,25,26,27,28,29,30,31,
+    32,33,34,35,36,37,38,39,
+    40,41,42,43,44,45,46,47};
+  # count of values = 48 = 12 * N * N
+  write;
+EOF
+${tools_dir}/grib_filter -o $tempGrib $tempFilt $input
+${tools_dir}/grib_get_data $tempGrib > $tempLog
+
+# Nested ordering: N must be a power of 2
+input=$ECCODES_SAMPLES_PATH/GRIB2.tmpl
+${tools_dir}/grib_set -s gridType=healpix,Nside=3,orderingConvention=nested,numberOfDataPoints=108,numberOfValues=108 $input $tempGrib
+set +e
+${tools_dir}/grib_get_data $tempGrib > $tempLog 2>&1
+status=$?
+set -e
+[ $status -ne 0 ]
+grep -q "Nside must be a power of 2" $tempLog
+
+
 # Invalid cases
 # --------------
 set +e
@@ -81,13 +114,6 @@ set -e
 [ $status -ne 0 ]
 grep -q "Nside must be greater than zero" $tempLog
 
-set +e
-${tools_dir}/grib_get_data -s orderingConvention=nested $tempGrib > $tempLog 2>&1
-status=$?
-set -e
-[ $status -ne 0 ]
-grep -q "Only ring ordering is supported" $tempLog
-
 
 # Clean up
 rm -f $tempFilt $tempGrib $tempLog