diff --git a/lib/grade/grade_category.php b/lib/grade/grade_category.php
index ca67450c4ab..10656f95c82 100644
--- a/lib/grade/grade_category.php
+++ b/lib/grade/grade_category.php
@@ -878,22 +878,66 @@ class grade_category extends grade_object {
             asort($grade_values, SORT_NUMERIC);
             $dropped = 0;
 
-            foreach ($grade_values as $itemid=>$value) {
+            // If we have fewer grade items available to drop than $this->droplow, use this flag to escape the loop
+            // May occur because of "extra credit" or if droplow is higher than the number of grade items
+            $droppedsomething = true;
 
-                if ($dropped < $this->droplow) {
+            while ($dropped < $this->droplow && $droppedsomething) {
+                $droppedsomething = false;
 
-                    if ($extraused and $items[$itemid]->aggregationcoef > 0) {
-                        // no drop low for extra credits
-
-                    } else {
-                        unset($grade_values[$itemid]);
-                        $dropped++;
-                    }
-
-                } else {
-                    // we have dropped enough
+                $grade_keys = array_keys($grade_values);
+                if (count($grade_keys) === 0) {
+                    //We've dropped all grade items
                     break;
                 }
+
+                $originalindex = $founditemid = $foundmax = null;
+
+                // Find the first remaining grade item that is available to be dropped
+                foreach ($grade_keys as $gradekeyindex=>$gradekey) {
+                    if (!$extraused || $items[$gradekey]->aggregationcoef <= 0) {
+                        // Found a non-extra credit grade item that is eligible to be dropped
+                        $originalindex = $gradekeyindex;
+                        $founditemid = $grade_keys[$originalindex];
+                        $foundmax = $items[$founditemid]->grademax;
+                        break;
+                    }
+                }
+
+                if (empty($founditemid)) {
+                    // No grade items available to drop
+                    break;
+                }
+
+                // Now iterate over the remaining grade items
+                // We're looking for other grade items with the same grade value but a higher grademax
+                $i = 1;
+                while ($originalindex+$i < count($grade_keys)) {
+                    $possibleitemid = $grade_keys[$originalindex+$i];
+                    if ($grade_values[$founditemid] != $grade_values[$possibleitemid]) {
+                        // The next grade item has a different grade value. Stop looking.
+                        break;
+                    }
+
+                    if ($extraused && $items[$possibleitemid]->aggregationcoef > 0) {
+                        // Don't drop extra credit grade items. Continue the search.
+                        continue;
+                    }
+
+                    if ($foundmax < $items[$possibleitemid]->grademax) {
+                        // Found a grade item with the same grade value and a higher grademax
+                        $foundmax = $items[$possibleitemid]->grademax;
+                        $founditemid = $possibleitemid;
+                        // Continue searching to see if there is an even higher grademax
+                    }
+
+                    $i++;
+                }
+
+                // Now drop whatever grade item we have found
+                unset($grade_values[$founditemid]);
+                $dropped++;
+                $droppedsomething = true;
             }
 
         } else if (!empty($this->keephigh)) {
diff --git a/lib/grade/tests/grade_category_test.php b/lib/grade/tests/grade_category_test.php
index 102ef8625c6..727e69867f0 100644
--- a/lib/grade/tests/grade_category_test.php
+++ b/lib/grade/tests/grade_category_test.php
@@ -406,6 +406,7 @@ class grade_category_testcase extends grade_base_testcase {
         $items[$this->grade_items[2]->id] = new grade_item($this->grade_items[2], false);
         $items[$this->grade_items[4]->id] = new grade_item($this->grade_items[4], false);
 
+        // Test excluding the lowest 2 out of 4 grades from aggregation with no 0 grades
         $category = new grade_category();
         $category->droplow = 2;
         $grades = array($this->grade_items[0]->id=>5.374,
@@ -417,6 +418,7 @@ class grade_category_testcase extends grade_base_testcase {
         $this->assertEquals($grades[$this->grade_items[1]->id], 9.4743);
         $this->assertEquals($grades[$this->grade_items[4]->id], 7.3754);
 
+        // Test aggregating only the highest 1 out of 4 grades
         $category = new grade_category();
         $category->keephigh = 1;
         $category->droplow = 0;
@@ -429,25 +431,28 @@ class grade_category_testcase extends grade_base_testcase {
         $grade = reset($grades);
         $this->assertEquals(9.4743, $grade);
 
+        // Test excluding the lowest 2 out of 4 grades from aggregation with no 0 grades
+        // An extra credit grade item should be kept even if droplow means it would otherwise be excluded
         $category = new grade_category();
         $category->droplow     = 2;
         $category->aggregation = GRADE_AGGREGATE_SUM;
-        $items[$this->grade_items[2]->id]->aggregationcoef = 1;
+        $items[$this->grade_items[2]->id]->aggregationcoef = 1; // Mark grade item 2 as "extra credit"
         $grades = array($this->grade_items[0]->id=>5.374,
                         $this->grade_items[1]->id=>9.4743,
                         $this->grade_items[2]->id=>2.5474,
                         $this->grade_items[4]->id=>7.3754);
-
         $category->apply_limit_rules($grades, $items);
         $this->assertEquals(count($grades), 2);
         $this->assertEquals($grades[$this->grade_items[1]->id], 9.4743);
         $this->assertEquals($grades[$this->grade_items[2]->id], 2.5474);
 
+        // Test only aggregating the highest 1 out of 4 grades
+        // An extra credit grade item is retained in addition to the highest grade
         $category = new grade_category();
         $category->keephigh = 1;
         $category->droplow = 0;
         $category->aggregation = GRADE_AGGREGATE_SUM;
-        $items[$this->grade_items[2]->id]->aggregationcoef = 1;
+        $items[$this->grade_items[2]->id]->aggregationcoef = 1; // Mark grade item 2 as "extra credit"
         $grades = array($this->grade_items[0]->id=>5.374,
                         $this->grade_items[1]->id=>9.4743,
                         $this->grade_items[2]->id=>2.5474,
@@ -456,6 +461,61 @@ class grade_category_testcase extends grade_base_testcase {
         $this->assertEquals(count($grades), 2);
         $this->assertEquals($grades[$this->grade_items[1]->id], 9.4743);
         $this->assertEquals($grades[$this->grade_items[2]->id], 2.5474);
+
+
+        // Test excluding the lowest 1 out of 4 grades from aggregation with two 0 grades
+        $items[$this->grade_items[2]->id]->aggregationcoef = 0; // Undo marking grade item 2 as "extra credit"
+        $category = new grade_category();
+        $category->droplow     = 1;
+        $category->aggregation = GRADE_AGGREGATE_WEIGHTED_MEAN2; // simple weighted mean
+        $grades = array($this->grade_items[0]->id=>0, // 0 out of 110. Should be excluded from aggregation.
+                        $this->grade_items[1]->id=>5, // 5 out of 100
+                        $this->grade_items[2]->id=>2, // 0 out of 6
+                        $this->grade_items[4]->id=>0); // 0 out of 100
+        $category->apply_limit_rules($grades, $items);
+        $this->assertEquals(count($grades), 3);
+        $this->assertEquals($grades[$this->grade_items[1]->id], 5);
+        $this->assertEquals($grades[$this->grade_items[2]->id], 2);
+        $this->assertEquals($grades[$this->grade_items[4]->id], 0);
+
+        // Test excluding the lowest 2 out of 4 grades from aggregation with three 0 grades
+        $category = new grade_category();
+        $category->droplow     = 2;
+        $category->aggregation = GRADE_AGGREGATE_WEIGHTED_MEAN2; // simple weighted mean
+        $grades = array($this->grade_items[0]->id=>0, // 0 out of 110. Should be excluded from aggregation.
+                        $this->grade_items[1]->id=>5, // 5 out of 100
+                        $this->grade_items[2]->id=>0, // 0 out of 6
+                        $this->grade_items[4]->id=>0); // 0 out of 100. Should be excluded from aggregation.
+        $category->apply_limit_rules($grades, $items);
+        $this->assertEquals(count($grades), 2);
+        $this->assertEquals($grades[$this->grade_items[1]->id], 5);
+        $this->assertEquals($grades[$this->grade_items[2]->id], 0);
+
+        // Test excluding the lowest 5 out of 4 grades from aggregation
+        // Just to check we handle this sensibly
+        $category = new grade_category();
+        $category->droplow     = 5;
+        $category->aggregation = GRADE_AGGREGATE_WEIGHTED_MEAN2; // simple weighted mean
+        $grades = array($this->grade_items[0]->id=>0, // 0 out of 110. Should be excluded from aggregation.
+                        $this->grade_items[1]->id=>5, // 5 out of 100
+                        $this->grade_items[2]->id=>6, // 6 out of 6
+                        $this->grade_items[4]->id=>1);// 1 out of 100. Should be excluded from aggregation.
+        $category->apply_limit_rules($grades, $items);
+        $this->assertEquals(count($grades), 0);
+
+        // Test excluding the lowest 4 out of 4 grades from aggregation with one marked as extra credit
+        $category = new grade_category();
+        $category->droplow     = 4;
+        $category->aggregation = GRADE_AGGREGATE_WEIGHTED_MEAN2; // simple weighted mean
+        $items[$this->grade_items[2]->id]->aggregationcoef = 1; // Mark grade item 2 as "extra credit"
+        $grades = array($this->grade_items[0]->id=>0, // 0 out of 110. Should be excluded from aggregation.
+                        $this->grade_items[1]->id=>5, // 5 out of 100. Should be excluded from aggregation.
+                        $this->grade_items[2]->id=>6, // 6 out of 6. Extra credit. Should be retained.
+                        $this->grade_items[4]->id=>1);// 1 out of 100. Should be excluded from aggregation.
+        $category->apply_limit_rules($grades, $items);
+        $this->assertEquals(count($grades), 1);
+        $this->assertEquals($grades[$this->grade_items[2]->id], 6);
+
     }
 
     /**