diff --git a/pkg/sql/colexec/colbuilder/execplan.go b/pkg/sql/colexec/colbuilder/execplan.go
index 6d017b9528f5..eb81e53f7585 100644
--- a/pkg/sql/colexec/colbuilder/execplan.go
+++ b/pkg/sql/colexec/colbuilder/execplan.go
@@ -810,31 +810,6 @@ func NewColOperator(
 				return r, err
 			}
 			aggSpec := core.Aggregator
-			if len(aggSpec.Aggregations) == 0 {
-				// We can get an aggregator when no aggregate functions are
-				// present if HAVING clause is present, for example, with a
-				// query as follows: SELECT 1 FROM t HAVING true. In this case,
-				// we plan a special operator that outputs a batch of length 1
-				// or 0 (depending on whether the aggregate is in scalar context
-				// or not) without actual columns once and then zero-length
-				// batches. The actual "data" will be added by projections
-				// below.
-				// TODO(solon): The distsql plan for this case includes a
-				// TableReader, so we end up creating an orphaned colBatchScan.
-				// We should avoid that. Ideally the optimizer would not plan a
-				// scan in this unusual case.
-				numTuples := 0
-				if aggSpec.IsScalar() {
-					numTuples = 1
-				}
-				result.Root, err = colexecutils.NewFixedNumTuplesNoInputOp(
-					getStreamingAllocator(ctx, args), numTuples, inputs[0].Root,
-				), nil
-				// We make ColumnTypes non-nil so that sanity check doesn't
-				// panic.
-				result.ColumnTypes = []*types.T{}
-				break
-			}
 			if aggSpec.IsRowCount() {
 				result.Root, err = colexec.NewCountOp(getStreamingAllocator(ctx, args), inputs[0].Root), nil
 				result.ColumnTypes = []*types.T{types.Int}
diff --git a/pkg/sql/colexec/colexecbase/distinct.go b/pkg/sql/colexec/colexecbase/distinct.go
index 998aadb59f1b..ba0510f4cba6 100644
--- a/pkg/sql/colexec/colexecbase/distinct.go
+++ b/pkg/sql/colexec/colexecbase/distinct.go
@@ -35,8 +35,19 @@ func OrderedDistinctColsToOperators(
 		OneInputHelper: colexecop.MakeOneInputHelper(input),
 		fn:             func() { copy(distinctCol, colexecutils.ZeroBoolColumn) },
 	}
-	for i := range distinctCols {
-		input = newSingleDistinct(input, int(distinctCols[i]), distinctCol, typs[distinctCols[i]], nullsAreDistinct)
+	if len(distinctCols) > 0 {
+		for i := range distinctCols {
+			input = newSingleDistinct(input, int(distinctCols[i]), distinctCol, typs[distinctCols[i]], nullsAreDistinct)
+		}
+	} else {
+		// If there are no distinct columns, we have to mark the very first
+		// tuple as distinct ourselves.
+		firstTuple := true
+		input.(*fnOp).fn = func() {
+			copy(distinctCol, colexecutils.ZeroBoolColumn)
+			distinctCol[0] = firstTuple
+			firstTuple = false
+		}
 	}
 	r, ok := input.(colexecop.ResettableOperator)
 	if !ok {
diff --git a/pkg/sql/colexec/ordered_aggregator.go b/pkg/sql/colexec/ordered_aggregator.go
index 76bef5d09007..83f81dce9e1c 100644
--- a/pkg/sql/colexec/ordered_aggregator.go
+++ b/pkg/sql/colexec/ordered_aggregator.go
@@ -255,7 +255,18 @@ func (a *orderedAggregator) Next() coldata.Batch {
 						}
 					})
 				}
-				a.scratch.resumeIdx = a.bucket.fns[0].CurrentOutputIndex()
+				if len(a.bucket.fns) > 0 {
+					a.scratch.resumeIdx = a.bucket.fns[0].CurrentOutputIndex()
+				} else {
+					// When there are no aggregate functions to compute, we
+					// simply need to output the same number of empty rows as
+					// the number of groups.
+					for _, newGroup := range a.groupCol[:batchLength] {
+						if newGroup {
+							a.scratch.resumeIdx++
+						}
+					}
+				}
 			}
 			if batchLength == 0 {
 				a.state = orderedAggregatorOutputting