diff --git a/src/backend/commands/analyze.c b/src/backend/commands/analyze.c
index 848263d3900..925d06ed8ce 100644
--- a/src/backend/commands/analyze.c
+++ b/src/backend/commands/analyze.c
@@ -1215,19 +1215,22 @@ acquire_sample_rows(Relation onerel, int elevel,
 		qsort((void *) rows, numrows, sizeof(HeapTuple), compare_rows);
 
 	/*
-	 * Estimate total numbers of rows in relation.  For live rows, use
-	 * vac_estimate_reltuples; for dead rows, we have no source of old
-	 * information, so we have to assume the density is the same in unseen
-	 * pages as in the pages we scanned.
+	 * Estimate total numbers of live and dead rows in relation, extrapolating
+	 * on the assumption that the average tuple density in pages we didn't
+	 * scan is the same as in the pages we did scan.  Since what we scanned is
+	 * a random sample of the pages in the relation, this should be a good
+	 * assumption.
 	 */
-	*totalrows = vac_estimate_reltuples(onerel, true,
-										totalblocks,
-										bs.m,
-										liverows);
 	if (bs.m > 0)
+	{
+		*totalrows = floor((liverows / bs.m) * totalblocks + 0.5);
 		*totaldeadrows = floor((deadrows / bs.m) * totalblocks + 0.5);
+	}
 	else
+	{
+		*totalrows = 0.0;
 		*totaldeadrows = 0.0;
+	}
 
 	/*
 	 * Emit some interesting relation info
diff --git a/src/backend/commands/vacuum.c b/src/backend/commands/vacuum.c
index d533cef6a6c..dd93ecb6046 100644
--- a/src/backend/commands/vacuum.c
+++ b/src/backend/commands/vacuum.c
@@ -685,13 +685,13 @@ vacuum_set_xid_limits(Relation rel,
  * vac_estimate_reltuples() -- estimate the new value for pg_class.reltuples
  *
  *		If we scanned the whole relation then we should just use the count of
- *		live tuples seen; but if we did not, we should not trust the count
- *		unreservedly, especially not in VACUUM, which may have scanned a quite
- *		nonrandom subset of the table.  When we have only partial information,
- *		we take the old value of pg_class.reltuples as a measurement of the
+ *		live tuples seen; but if we did not, we should not blindly extrapolate
+ *		from that number, since VACUUM may have scanned a quite nonrandom
+ *		subset of the table.  When we have only partial information, we take
+ *		the old value of pg_class.reltuples as a measurement of the
  *		tuple density in the unscanned pages.
  *
- *		This routine is shared by VACUUM and ANALYZE.
+ *		The is_analyze argument is historical.
  */
 double
 vac_estimate_reltuples(Relation relation, bool is_analyze,
@@ -702,9 +702,8 @@ vac_estimate_reltuples(Relation relation, bool is_analyze,
 	BlockNumber old_rel_pages = relation->rd_rel->relpages;
 	double		old_rel_tuples = relation->rd_rel->reltuples;
 	double		old_density;
-	double		new_density;
-	double		multiplier;
-	double		updated_density;
+	double		unscanned_pages;
+	double		total_tuples;
 
 	/* If we did scan the whole table, just use the count as-is */
 	if (scanned_pages >= total_pages)
@@ -728,31 +727,14 @@ vac_estimate_reltuples(Relation relation, bool is_analyze,
 
 	/*
 	 * Okay, we've covered the corner cases.  The normal calculation is to
-	 * convert the old measurement to a density (tuples per page), then update
-	 * the density using an exponential-moving-average approach, and finally
-	 * compute reltuples as updated_density * total_pages.
-	 *
-	 * For ANALYZE, the moving average multiplier is just the fraction of the
-	 * table's pages we scanned.  This is equivalent to assuming that the
-	 * tuple density in the unscanned pages didn't change.  Of course, it
-	 * probably did, if the new density measurement is different. But over
-	 * repeated cycles, the value of reltuples will converge towards the
-	 * correct value, if repeated measurements show the same new density.
-	 *
-	 * For VACUUM, the situation is a bit different: we have looked at a
-	 * nonrandom sample of pages, but we know for certain that the pages we
-	 * didn't look at are precisely the ones that haven't changed lately.
-	 * Thus, there is a reasonable argument for doing exactly the same thing
-	 * as for the ANALYZE case, that is use the old density measurement as the
-	 * value for the unscanned pages.
-	 *
-	 * This logic could probably use further refinement.
+	 * convert the old measurement to a density (tuples per page), then
+	 * estimate the number of tuples in the unscanned pages using that figure,
+	 * and finally add on the number of tuples in the scanned pages.
 	 */
 	old_density = old_rel_tuples / old_rel_pages;
-	new_density = scanned_tuples / scanned_pages;
-	multiplier = (double) scanned_pages / (double) total_pages;
-	updated_density = old_density + (new_density - old_density) * multiplier;
-	return floor(updated_density * total_pages + 0.5);
+	unscanned_pages = (double) total_pages - (double) scanned_pages;
+	total_tuples = old_density * unscanned_pages + scanned_tuples;
+	return floor(total_tuples + 0.5);
 }