diff --git a/c/CHANGELOG.rst b/c/CHANGELOG.rst
index 32fd205cef..b2d48a1c03 100644
--- a/c/CHANGELOG.rst
+++ b/c/CHANGELOG.rst
@@ -8,6 +8,11 @@
   nodes of each node in the tree. (:user:`GertjanBisschop`, :issue:`2274`, :pr:`2316`)
 
 
+**Changes**
+
+- Reduce the maximum number of rows in a table by 1. This removes edge cases so that a ``tsk_id_t`` can be
+  used to count the number of rows. (:user:`benjeffery`, :issue:`2336`, :pr:`2337`)
+
 --------------------
 [1.0.0] - 2022-05-24
 --------------------
diff --git a/c/tests/test_tables.c b/c/tests/test_tables.c
index 8da440ed33..aa7280e45f 100644
--- a/c/tests/test_tables.c
+++ b/c/tests/test_tables.c
@@ -5927,7 +5927,7 @@ test_table_expansion(void)
 
     /*Extending by more rows than possible results in overflow*/
     ret = tsk_individual_table_extend(
-        &tables.individuals, &tables2.individuals, TSK_MAX_ID + 1, NULL, 0);
+        &tables.individuals, &tables2.individuals, TSK_MAX_ID, NULL, 0);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_TABLE_OVERFLOW);
     CU_ASSERT_EQUAL_FATAL(tables.individuals.max_rows, 4194305);
 
@@ -5986,7 +5986,7 @@ test_table_expansion(void)
     CU_ASSERT_EQUAL_FATAL(tables.nodes.max_rows, 4194305);
 
     /*Extending by more rows than possible results in overflow*/
-    ret = tsk_node_table_extend(&tables.nodes, &tables2.nodes, TSK_MAX_ID + 1, NULL, 0);
+    ret = tsk_node_table_extend(&tables.nodes, &tables2.nodes, TSK_MAX_ID, NULL, 0);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_TABLE_OVERFLOW);
     CU_ASSERT_EQUAL_FATAL(tables.nodes.max_rows, 4194305);
 
@@ -6044,7 +6044,7 @@ test_table_expansion(void)
     CU_ASSERT_EQUAL_FATAL(tables.edges.max_rows, 4194305);
 
     /*Extending by more rows than possible results in overflow*/
-    ret = tsk_edge_table_extend(&tables.edges, &tables2.edges, TSK_MAX_ID + 1, NULL, 0);
+    ret = tsk_edge_table_extend(&tables.edges, &tables2.edges, TSK_MAX_ID, NULL, 0);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_TABLE_OVERFLOW);
     CU_ASSERT_EQUAL_FATAL(tables.edges.max_rows, 4194305);
 
@@ -6109,7 +6109,7 @@ test_table_expansion(void)
 
     /*Extending by more rows than possible results in overflow*/
     ret = tsk_migration_table_extend(
-        &tables.migrations, &tables2.migrations, TSK_MAX_ID + 1, NULL, 0);
+        &tables.migrations, &tables2.migrations, TSK_MAX_ID, NULL, 0);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_TABLE_OVERFLOW);
     CU_ASSERT_EQUAL_FATAL(tables.migrations.max_rows, 4194305);
 
@@ -6168,7 +6168,7 @@ test_table_expansion(void)
     CU_ASSERT_EQUAL_FATAL(tables.sites.max_rows, 4194305);
 
     /*Extending by more rows than possible results in overflow*/
-    ret = tsk_site_table_extend(&tables.sites, &tables2.sites, TSK_MAX_ID + 1, NULL, 0);
+    ret = tsk_site_table_extend(&tables.sites, &tables2.sites, TSK_MAX_ID, NULL, 0);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_TABLE_OVERFLOW);
     CU_ASSERT_EQUAL_FATAL(tables.sites.max_rows, 4194305);
 
@@ -6232,7 +6232,7 @@ test_table_expansion(void)
 
     /*Extending by more rows than possible results in overflow*/
     ret = tsk_mutation_table_extend(
-        &tables.mutations, &tables2.mutations, TSK_MAX_ID + 1, NULL, 0);
+        &tables.mutations, &tables2.mutations, TSK_MAX_ID, NULL, 0);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_TABLE_OVERFLOW);
     CU_ASSERT_EQUAL_FATAL(tables.mutations.max_rows, 4194305);
 
@@ -6298,7 +6298,7 @@ test_table_expansion(void)
 
     /*Extending by more rows than possible results in overflow*/
     ret = tsk_population_table_extend(
-        &tables.populations, &tables2.populations, TSK_MAX_ID + 1, NULL, 0);
+        &tables.populations, &tables2.populations, TSK_MAX_ID, NULL, 0);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_TABLE_OVERFLOW);
     CU_ASSERT_EQUAL_FATAL(tables.populations.max_rows, 4194305);
 
@@ -6364,7 +6364,7 @@ test_table_expansion(void)
 
     /*Extending by more rows than possible results in overflow*/
     ret = tsk_provenance_table_extend(
-        &tables.provenances, &tables2.provenances, TSK_MAX_ID + 1, NULL, 0);
+        &tables.provenances, &tables2.provenances, TSK_MAX_ID, NULL, 0);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_TABLE_OVERFLOW);
     CU_ASSERT_EQUAL_FATAL(tables.provenances.max_rows, 4194305);
 
@@ -8576,7 +8576,7 @@ test_table_overflow(void)
     int ret;
     tsk_id_t ret_id;
     tsk_table_collection_t tables;
-    tsk_size_t max_rows = ((tsk_size_t) TSK_MAX_ID) + 1;
+    tsk_size_t max_rows = ((tsk_size_t) TSK_MAX_ID);
 
     ret = tsk_table_collection_init(&tables, 0);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
diff --git a/c/tskit/tables.c b/c/tskit/tables.c
index b650b478bc..ee628d24f0 100644
--- a/c/tskit/tables.c
+++ b/c/tskit/tables.c
@@ -79,13 +79,14 @@ typedef struct {
 } write_table_ragged_col_t;
 
 /* Returns true if adding the specified number of rows would result in overflow.
- * Tables can support indexes from 0 to TSK_MAX_ID, and therefore have at most
- * TSK_MAX_ID + 1 rows */
+ * Tables can support indexes from 0 to TSK_MAX_ID, and therefore could have at most
+ * TSK_MAX_ID + 1 rows. However we limit to TSK_MAX_ID rows so that counts of rows
+ * can fit in a tsk_id_t. */
 static bool
 check_table_overflow(tsk_size_t current_size, tsk_size_t additional_rows)
 {
-    tsk_size_t max_val = TSK_MAX_ID + (tsk_size_t) 1;
-    return current_size > (max_val - additional_rows);
+    tsk_size_t max_val = TSK_MAX_ID;
+    return additional_rows > max_val || current_size > (max_val - additional_rows);
 }
 
 /* Returns true if adding the specified number of elements would result in overflow
@@ -94,7 +95,9 @@ check_table_overflow(tsk_size_t current_size, tsk_size_t additional_rows)
 static bool
 check_offset_overflow(tsk_size_t current_size, tsk_size_t additional_elements)
 {
-    return current_size > (TSK_MAX_SIZE - additional_elements);
+    tsk_size_t max_val = TSK_MAX_SIZE;
+    return additional_elements > max_val
+           || current_size > (max_val - additional_elements);
 }
 
 #define TSK_NUM_ROWS_UNSET ((tsk_size_t) -1)