diff --git a/x-pack/plugin/sql/src/main/java/org/elasticsearch/xpack/sql/analysis/analyzer/Verifier.java b/x-pack/plugin/sql/src/main/java/org/elasticsearch/xpack/sql/analysis/analyzer/Verifier.java
index 6f8be61b463fd..4915a25a55bc7 100644
--- a/x-pack/plugin/sql/src/main/java/org/elasticsearch/xpack/sql/analysis/analyzer/Verifier.java
+++ b/x-pack/plugin/sql/src/main/java/org/elasticsearch/xpack/sql/analysis/analyzer/Verifier.java
@@ -213,10 +213,11 @@ static Collection<Failure> verify(LogicalPlan plan) {
      * Check validity of Aggregate/GroupBy.
      * This rule is needed for multiple reasons:
      * 1. a user might specify an invalid aggregate (SELECT foo GROUP BY bar)
-     * 2. the order/having might contain a non-grouped attribute. This is typically
+     * 2. the ORDER BY/HAVING might contain a non-grouped attribute. This is typically
      * caught by the Analyzer however if wrapped in a function (ABS()) it gets resolved
      * (because the expression gets resolved little by little without being pushed down,
      * without the Analyzer modifying anything.
+     * 2a. HAVING also requires an Aggregate function
      * 3. composite agg (used for GROUP BY) allows ordering only on the group keys
      */
     private static boolean checkGroupBy(LogicalPlan p, Set<Failure> localFailures,
@@ -244,7 +245,7 @@ private static boolean checkGroupByOrder(LogicalPlan p, Set<Failure> localFailur
                     }
 
                     // make sure to compare attributes directly
-                    if (Expressions.anyMatch(a.groupings(), 
+                    if (Expressions.anyMatch(a.groupings(),
                             g -> e.semanticEquals(e instanceof Attribute ? Expressions.attribute(g) : g))) {
                         return;
                     }
@@ -278,13 +279,14 @@ private static boolean checkGroupByHaving(LogicalPlan p, Set<Failure> localFailu
 
                 Map<Expression, Node<?>> missing = new LinkedHashMap<>();
                 Expression condition = f.condition();
-                condition.collectFirstChildren(c -> checkGroupMatch(c, condition, a.groupings(), missing, functions));
+                // variation of checkGroupMatch customized for HAVING, which requires just aggregations
+                condition.collectFirstChildren(c -> checkGroupByHavingHasOnlyAggs(c, condition, missing, functions));
 
                 if (!missing.isEmpty()) {
                     String plural = missing.size() > 1 ? "s" : StringUtils.EMPTY;
-                    localFailures.add(fail(condition, "Cannot filter by non-grouped column" + plural + " %s, expected %s",
-                            Expressions.names(missing.keySet()),
-                            Expressions.names(a.groupings())));
+                    localFailures.add(
+                            fail(condition, "Cannot filter HAVING on non-aggregate" + plural + " %s; consider using WHERE instead",
+                            Expressions.names(missing.keySet())));
                     groupingFailures.add(a);
                     return false;
                 }
@@ -294,6 +296,57 @@ private static boolean checkGroupByHaving(LogicalPlan p, Set<Failure> localFailu
     }
 
 
+    private static boolean checkGroupByHavingHasOnlyAggs(Expression e, Node<?> source,
+            Map<Expression, Node<?>> missing, Map<String, Function> functions) {
+
+        // resolve FunctionAttribute to backing functions
+        if (e instanceof FunctionAttribute) {
+            FunctionAttribute fa = (FunctionAttribute) e;
+            Function function = functions.get(fa.functionId());
+            // TODO: this should be handled by a different rule
+            if (function == null) {
+                return false;
+            }
+            e = function;
+        }
+
+        // scalar functions can be a binary tree
+        // first test the function against the grouping
+        // and if that fails, start unpacking hoping to find matches
+        if (e instanceof ScalarFunction) {
+            ScalarFunction sf = (ScalarFunction) e;
+
+            // unwrap function to find the base
+            for (Expression arg : sf.arguments()) {
+                arg.collectFirstChildren(c -> checkGroupByHavingHasOnlyAggs(c, source, missing, functions));
+            }
+            return true;
+
+        } else if (e instanceof Score) {
+            // Score can't be used for having
+            missing.put(e, source);
+            return true;
+        }
+
+        // skip literals / foldable
+        if (e.foldable()) {
+            return true;
+        }
+        // skip aggs (allowed to refer to non-group columns)
+        if (Functions.isAggregate(e)) {
+            return true;
+        }
+
+        // left without leaves which have to match; that's a failure since everything should be based on an agg
+        if (e instanceof Attribute) {
+            missing.put(e, source);
+            return true;
+        }
+
+        return false;
+    }
+
+
     // check whether plain columns specified in an agg are mentioned in the group-by
     private static boolean checkGroupByAgg(LogicalPlan p, Set<Failure> localFailures,
             Set<LogicalPlan> groupingFailures, Map<String, Function> functions) {
diff --git a/x-pack/plugin/sql/src/test/java/org/elasticsearch/xpack/sql/analysis/analyzer/VerifierErrorMessagesTests.java b/x-pack/plugin/sql/src/test/java/org/elasticsearch/xpack/sql/analysis/analyzer/VerifierErrorMessagesTests.java
index 60875e0194a0c..dce665a97e95d 100644
--- a/x-pack/plugin/sql/src/test/java/org/elasticsearch/xpack/sql/analysis/analyzer/VerifierErrorMessagesTests.java
+++ b/x-pack/plugin/sql/src/test/java/org/elasticsearch/xpack/sql/analysis/analyzer/VerifierErrorMessagesTests.java
@@ -159,4 +159,14 @@ public void testGroupByOrderByScore() {
         assertEquals("1:44: Cannot order by non-grouped column [SCORE()], expected [int]",
                 verify("SELECT int FROM test GROUP BY int ORDER BY SCORE()"));
     }
+
+    public void testHavingOnColumn() {
+        assertEquals("1:42: Cannot filter HAVING on non-aggregate [int]; consider using WHERE instead",
+                verify("SELECT int FROM test GROUP BY int HAVING int > 2"));
+    }
+
+    public void testHavingOnScalar() {
+        assertEquals("1:42: Cannot filter HAVING on non-aggregate [int]; consider using WHERE instead",
+                verify("SELECT int FROM test GROUP BY int HAVING 2 < ABS(int)"));
+    }
 }
\ No newline at end of file