diff --git a/c/CHANGELOG.rst b/c/CHANGELOG.rst
index 9f8ed69789..74065da930 100644
--- a/c/CHANGELOG.rst
+++ b/c/CHANGELOG.rst
@@ -13,6 +13,10 @@
 - Rename TSK_TAKE_TABLES to TSK_TAKE_OWNERSHIP.
   (:user:`benjeffery`, :issue:`2221`, :pr:`2222`)
 
+- Rename all flags to ``simplify`` for example ``TSK_KEEP_INPUT_ROOTS`` becomes ``TSK_SIMPLIFY_KEEP_INPUT_ROOTS``
+  (:user:`benjeffery`, :issue:`1720`, :pr:`2226`))
+
+
 **Features**
 
 - Make dumping of tables and tree sequences to disk a zero-copy operation.
@@ -199,7 +203,7 @@ Minor bugfix on internal APIs
 
 **Features**
 
-- Add ``TSK_KEEP_UNARY_IN_INDIVIDUALS`` flag to simplify, which allows the user to
+- Add ``TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS`` flag to simplify, which allows the user to
   keep unary nodes only if they belong to a tabled individual. This is useful for
   simplification in forwards simulations (:user:`hyanwong`, :issue:`1113`, :pr:`1119`).
 
@@ -249,7 +253,7 @@ Minor bugfix on internal APIs
 **Bugfixes**
 
 - :issue:`823` - Fix mutation time error when using
-  ``tsk_table_collection_simplify`` with ``TSK_KEEP_INPUT_ROOTS``
+  ``tsk_table_collection_simplify`` with ``TSK_SIMPLIFY_KEEP_INPUT_ROOTS``
   (:user:`petrelharp`, :pr:`823`).
 
 ---------------------
@@ -263,7 +267,7 @@ Minor bugfix on internal APIs
 
 **New features**
 
-- Add a ``TSK_KEEP_INPUT_ROOTS`` option to simplify which, if enabled, adds edges
+- Add a ``TSK_SIMPLIFY_KEEP_INPUT_ROOTS`` option to simplify which, if enabled, adds edges
   from the MRCAs of samples in the simplified tree sequence back to the roots
   in the input tree sequence (:user:`jeromekelleher`, :issue:`775`, :pr:`782`).
 
@@ -357,7 +361,7 @@ Minor bugfix on internal APIs
   tree sequence. These store arbitrary bytes and are optional in the file format.
   (:user: `benjeffery`, :pr:`641`)
 
-- Add the ``TSK_KEEP_UNARY`` option to simplify (:user:`gtsambos`). See :issue:`1`
+- Add the ``TSK_SIMPLIFY_KEEP_UNARY`` option to simplify (:user:`gtsambos`). See :issue:`1`
   and :pr:`143`.
 
 - Add a ``set_root_threshold`` option to tsk_tree_t which allows us to set the
diff --git a/c/tests/test_trees.c b/c/tests/test_trees.c
index e58b0ac1e6..2bca1f3112 100644
--- a/c/tests/test_trees.c
+++ b/c/tests/test_trees.c
@@ -654,7 +654,7 @@ verify_simplify(tsk_treeseq_t *ts)
     const tsk_id_t *sample;
     tsk_id_t *node_map = tsk_malloc(tsk_treeseq_get_num_nodes(ts) * sizeof(tsk_id_t));
     tsk_treeseq_t subset;
-    tsk_flags_t options = TSK_FILTER_SITES;
+    tsk_flags_t options = TSK_SIMPLIFY_FILTER_SITES;
 
     CU_ASSERT_FATAL(node_map != NULL);
     sample = tsk_treeseq_get_samples(ts);
@@ -1118,17 +1118,19 @@ test_simplest_records(void)
     tsk_treeseq_free(&simplified);
 
     ret = tsk_treeseq_simplify(&ts, sample_ids, 2,
-        TSK_KEEP_UNARY | TSK_KEEP_UNARY_IN_INDIVIDUALS, &simplified, NULL);
+        TSK_SIMPLIFY_KEEP_UNARY | TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS, &simplified,
+        NULL);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_KEEP_UNARY_MUTUALLY_EXCLUSIVE);
     tsk_treeseq_free(&simplified);
 
-    ret = tsk_treeseq_simplify(&ts, sample_ids, 2, TSK_KEEP_UNARY, &simplified, NULL);
+    ret = tsk_treeseq_simplify(
+        &ts, sample_ids, 2, TSK_SIMPLIFY_KEEP_UNARY, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
 
     ret = tsk_treeseq_simplify(
-        &ts, sample_ids, 2, TSK_KEEP_UNARY_IN_INDIVIDUALS, &simplified, NULL);
+        &ts, sample_ids, 2, TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
@@ -1161,13 +1163,14 @@ test_simplest_nonbinary_records(void)
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
 
-    ret = tsk_treeseq_simplify(&ts, sample_ids, 4, TSK_KEEP_UNARY, &simplified, NULL);
+    ret = tsk_treeseq_simplify(
+        &ts, sample_ids, 4, TSK_SIMPLIFY_KEEP_UNARY, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
 
     ret = tsk_treeseq_simplify(
-        &ts, sample_ids, 4, TSK_KEEP_UNARY_IN_INDIVIDUALS, &simplified, NULL);
+        &ts, sample_ids, 4, TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
@@ -1208,13 +1211,14 @@ test_simplest_unary_records(void)
     CU_ASSERT_EQUAL(tsk_treeseq_get_num_trees(&simplified), 1);
     tsk_treeseq_free(&simplified);
 
-    ret = tsk_treeseq_simplify(&ts, sample_ids, 2, TSK_KEEP_UNARY, &simplified, NULL);
+    ret = tsk_treeseq_simplify(
+        &ts, sample_ids, 2, TSK_SIMPLIFY_KEEP_UNARY, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
 
     ret = tsk_treeseq_simplify(
-        &ts, sample_ids, 2, TSK_KEEP_UNARY_IN_INDIVIDUALS, &simplified, NULL);
+        &ts, sample_ids, 2, TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_FALSE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     ret = tsk_treeseq_simplify(&ts, sample_ids, 2, 0, &simplified_other, NULL);
@@ -1285,7 +1289,8 @@ test_simplest_unary_with_individuals(void)
     CU_ASSERT_EQUAL(tsk_treeseq_get_num_populations(&ts), 1);
 
     ret = tsk_treeseq_simplify(&ts, sample_ids, 2,
-        TSK_KEEP_UNARY_IN_INDIVIDUALS | TSK_FILTER_INDIVIDUALS, &simplified, NULL);
+        TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS | TSK_SIMPLIFY_FILTER_INDIVIDUALS,
+        &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_TRUE(tsk_table_collection_equals(simplified.tables, expected.tables, 0));
     tsk_treeseq_free(&simplified);
@@ -1410,7 +1415,8 @@ test_simplest_degenerate_multiple_root_records(void)
     CU_ASSERT_EQUAL(tsk_treeseq_get_num_nodes(&simplified), 2);
     tsk_treeseq_free(&simplified);
 
-    ret = tsk_treeseq_simplify(&ts, sample_ids, 2, TSK_KEEP_UNARY, &simplified, NULL);
+    ret = tsk_treeseq_simplify(
+        &ts, sample_ids, 2, TSK_SIMPLIFY_KEEP_UNARY, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
@@ -1745,7 +1751,8 @@ test_simplest_holey_tree_sequence(void)
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
 
-    ret = tsk_treeseq_simplify(&ts, sample_ids, 2, TSK_KEEP_UNARY, &simplified, NULL);
+    ret = tsk_treeseq_simplify(
+        &ts, sample_ids, 2, TSK_SIMPLIFY_KEEP_UNARY, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
@@ -1837,7 +1844,8 @@ test_simplest_initial_gap_tree_sequence(void)
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
 
-    ret = tsk_treeseq_simplify(&ts, sample_ids, 2, TSK_KEEP_UNARY, &simplified, NULL);
+    ret = tsk_treeseq_simplify(
+        &ts, sample_ids, 2, TSK_SIMPLIFY_KEEP_UNARY, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_TRUE(tsk_table_collection_equals(ts.tables, simplified.tables, 0));
     tsk_treeseq_free(&simplified);
@@ -2899,7 +2907,7 @@ test_simplest_reduce_site_topology(void)
     CU_ASSERT_EQUAL_FATAL(tables.sites.num_rows, 1);
 
     ret = tsk_table_collection_simplify(
-        &tables, samples, 2, TSK_REDUCE_TO_SITE_TOPOLOGY, NULL);
+        &tables, samples, 2, TSK_SIMPLIFY_REDUCE_TO_SITE_TOPOLOGY, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
 
     CU_ASSERT_EQUAL(tables.nodes.num_rows, 3);
@@ -3006,7 +3014,7 @@ test_simplest_population_filter(void)
     CU_ASSERT_EQUAL(tables.populations.metadata[2], '2');
 
     ret = tsk_table_collection_simplify(
-        &tables, samples, 2, TSK_FILTER_POPULATIONS, NULL);
+        &tables, samples, 2, TSK_SIMPLIFY_FILTER_POPULATIONS, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_EQUAL(tables.nodes.num_rows, 2);
     CU_ASSERT_EQUAL(tables.nodes.population[0], 0);
@@ -3044,7 +3052,7 @@ test_simplest_individual_filter(void)
     CU_ASSERT_EQUAL(tables.individuals.metadata[2], '2');
 
     ret = tsk_table_collection_simplify(
-        &tables, samples, 2, TSK_FILTER_INDIVIDUALS, NULL);
+        &tables, samples, 2, TSK_SIMPLIFY_FILTER_INDIVIDUALS, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_EQUAL(tables.nodes.num_rows, 2);
     CU_ASSERT_EQUAL(tables.nodes.individual[0], 0);
@@ -4165,7 +4173,8 @@ test_single_tree_simplify_keep_input_roots(void)
     ret = tsk_treeseq_copy_tables(&ts, &tables, 0);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
 
-    ret = tsk_table_collection_simplify(&tables, samples, 2, TSK_KEEP_INPUT_ROOTS, NULL);
+    ret = tsk_table_collection_simplify(
+        &tables, samples, 2, TSK_SIMPLIFY_KEEP_INPUT_ROOTS, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     CU_ASSERT_EQUAL(tables.nodes.num_rows, 4);
     CU_ASSERT_EQUAL(tables.edges.num_rows, 3);
@@ -4948,7 +4957,8 @@ test_simplify_keep_input_roots_multi_tree(void)
     tsk_treeseq_from_text(&ts, 10, paper_ex_nodes, paper_ex_edges, NULL, paper_ex_sites,
         paper_ex_mutations, paper_ex_individuals, NULL, 0);
     tsk_treeseq_dump(&ts, "tmp.trees", 0);
-    ret = tsk_treeseq_simplify(&ts, samples, 2, TSK_KEEP_INPUT_ROOTS, &simplified, NULL);
+    ret = tsk_treeseq_simplify(
+        &ts, samples, 2, TSK_SIMPLIFY_KEEP_INPUT_ROOTS, &simplified, NULL);
     CU_ASSERT_EQUAL_FATAL(ret, 0);
     verify_trees(&simplified, num_trees, parents);
 
diff --git a/c/tskit/tables.c b/c/tskit/tables.c
index 7f1b292f1d..bb389140b3 100644
--- a/c/tskit/tables.c
+++ b/c/tskit/tables.c
@@ -1,7 +1,7 @@
 /*
  * MIT License
  *
- * Copyright (c) 2019-2021 Tskit Developers
+ * Copyright (c) 2019-2022 Tskit Developers
  * Copyright (c) 2017-2018 University of Oxford
  *
  * Permission is hereby granted, free of charge, to any person obtaining a copy
@@ -8660,14 +8660,15 @@ simplifier_print_state(simplifier_t *self, FILE *out)
     fprintf(out, "--simplifier state--\n");
     fprintf(out, "options:\n");
     fprintf(out, "\tfilter_unreferenced_sites   : %d\n",
-        !!(self->options & TSK_FILTER_SITES));
+        !!(self->options & TSK_SIMPLIFY_FILTER_SITES));
     fprintf(out, "\treduce_to_site_topology : %d\n",
-        !!(self->options & TSK_REDUCE_TO_SITE_TOPOLOGY));
-    fprintf(out, "\tkeep_unary              : %d\n", !!(self->options & TSK_KEEP_UNARY));
+        !!(self->options & TSK_SIMPLIFY_REDUCE_TO_SITE_TOPOLOGY));
+    fprintf(out, "\tkeep_unary              : %d\n",
+        !!(self->options & TSK_SIMPLIFY_KEEP_UNARY));
     fprintf(out, "\tkeep_input_roots        : %d\n",
-        !!(self->options & TSK_KEEP_INPUT_ROOTS));
+        !!(self->options & TSK_SIMPLIFY_KEEP_INPUT_ROOTS));
     fprintf(out, "\tkeep_unary_in_individuals : %d\n",
-        !!(self->options & TSK_KEEP_UNARY_IN_INDIVIDUALS));
+        !!(self->options & TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS));
 
     fprintf(out, "===\nInput tables\n==\n");
     tsk_table_collection_print_state(&self->input_tables, out);
@@ -8723,7 +8724,7 @@ simplifier_print_state(simplifier_t *self, FILE *out)
             fprintf(out, "]\n");
         }
     }
-    if (!!(self->options & TSK_REDUCE_TO_SITE_TOPOLOGY)) {
+    if (!!(self->options & TSK_SIMPLIFY_REDUCE_TO_SITE_TOPOLOGY)) {
         fprintf(out, "===\nposition_lookup\n==\n");
         for (j = 0; j < self->input_tables.sites.num_rows + 2; j++) {
             fprintf(out, "%lld\t-> %f\n", (long long) j, self->position_lookup[j]);
@@ -8883,7 +8884,7 @@ simplifier_record_edge(simplifier_t *self, double left, double right, tsk_id_t c
     interval_list_t *tail, *x;
     bool skip;
 
-    if (!!(self->options & TSK_REDUCE_TO_SITE_TOPOLOGY)) {
+    if (!!(self->options & TSK_SIMPLIFY_REDUCE_TO_SITE_TOPOLOGY)) {
         skip = simplifier_map_reduced_coordinates(self, &left, &right);
         /* NOTE: we exit early here when reduce_coordindates has told us to
          * skip this edge, as it is not visible in the reduced tree sequence */
@@ -9073,7 +9074,7 @@ simplifier_init(simplifier_t *self, const tsk_id_t *samples, tsk_size_t num_samp
     /* TODO Current unit tests require TSK_CHECK_SITE_DUPLICATES but it's
      * debateable whether we need it. If we remove, we definitely need explicit
      * tests to ensure we're doing sensible things with duplicate sites.
-     * (Particularly, re TSK_REDUCE_TO_SITE_TOPOLOGY.) */
+     * (Particularly, re TSK_SIMPLIFY_REDUCE_TO_SITE_TOPOLOGY.) */
     ret_id = tsk_table_collection_check_integrity(tables,
         TSK_CHECK_EDGE_ORDERING | TSK_CHECK_SITE_ORDERING | TSK_CHECK_SITE_DUPLICATES);
     if (ret_id != 0) {
@@ -9141,7 +9142,7 @@ simplifier_init(simplifier_t *self, const tsk_id_t *samples, tsk_size_t num_samp
     if (ret != 0) {
         goto out;
     }
-    if (!!(self->options & TSK_REDUCE_TO_SITE_TOPOLOGY)) {
+    if (!!(self->options & TSK_SIMPLIFY_REDUCE_TO_SITE_TOPOLOGY)) {
         ret = simplifier_init_position_lookup(self);
         if (ret != 0) {
             goto out;
@@ -9218,10 +9219,10 @@ simplifier_merge_ancestors(simplifier_t *self, tsk_id_t input_id)
 
     bool is_sample = output_id != TSK_NULL;
     bool keep_unary = false;
-    if (self->options & TSK_KEEP_UNARY) {
+    if (self->options & TSK_SIMPLIFY_KEEP_UNARY) {
         keep_unary = true;
     }
-    if ((self->options & TSK_KEEP_UNARY_IN_INDIVIDUALS)
+    if ((self->options & TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS)
         && (self->input_tables.nodes.individual[input_id] != TSK_NULL)) {
         keep_unary = true;
     }
@@ -9428,7 +9429,7 @@ simplifier_output_sites(simplifier_t *self)
     tsk_id_t num_output_mutations, num_output_site_mutations;
     tsk_id_t mapped_node;
     bool keep_site;
-    bool filter_sites = !!(self->options & TSK_FILTER_SITES);
+    bool filter_sites = !!(self->options & TSK_SIMPLIFY_FILTER_SITES);
     tsk_site_t site;
     tsk_mutation_t mutation;
 
@@ -9516,7 +9517,7 @@ simplifier_finalise_references(simplifier_t *self)
         = tsk_calloc(num_populations, sizeof(*population_referenced));
     tsk_id_t *population_id_map
         = tsk_malloc(num_populations * sizeof(*population_id_map));
-    bool filter_populations = !!(self->options & TSK_FILTER_POPULATIONS);
+    bool filter_populations = !!(self->options & TSK_SIMPLIFY_FILTER_POPULATIONS);
 
     tsk_individual_t ind;
     tsk_id_t ind_id;
@@ -9526,7 +9527,7 @@ simplifier_finalise_references(simplifier_t *self)
         = tsk_calloc(num_individuals, sizeof(*individual_referenced));
     tsk_id_t *individual_id_map
         = tsk_malloc(num_individuals * sizeof(*individual_id_map));
-    bool filter_individuals = !!(self->options & TSK_FILTER_INDIVIDUALS);
+    bool filter_individuals = !!(self->options & TSK_SIMPLIFY_FILTER_INDIVIDUALS);
 
     if (population_referenced == NULL || population_id_map == NULL
         || individual_referenced == NULL || individual_id_map == NULL) {
@@ -9729,7 +9730,7 @@ simplifier_run(simplifier_t *self, tsk_id_t *node_map)
             goto out;
         }
     }
-    if (self->options & TSK_KEEP_INPUT_ROOTS) {
+    if (self->options & TSK_SIMPLIFY_KEEP_INPUT_ROOTS) {
         ret = simplifier_insert_input_roots(self);
         if (ret != 0) {
             goto out;
@@ -9749,7 +9750,7 @@ simplifier_run(simplifier_t *self, tsk_id_t *node_map)
             self->input_tables.nodes.num_rows * sizeof(tsk_id_t));
     }
     if (self->edge_sort_offset != TSK_NULL) {
-        tsk_bug_assert(self->options & TSK_KEEP_INPUT_ROOTS);
+        tsk_bug_assert(self->options & TSK_SIMPLIFY_KEEP_INPUT_ROOTS);
         ret = simplifier_sort_edges(self);
         if (ret != 0) {
             goto out;
@@ -11446,7 +11447,8 @@ tsk_table_collection_simplify(tsk_table_collection_t *self, const tsk_id_t *samp
     /* Avoid calling to simplifier_free with uninit'd memory on error branches */
     tsk_memset(&simplifier, 0, sizeof(simplifier_t));
 
-    if ((options & TSK_KEEP_UNARY) && (options & TSK_KEEP_UNARY_IN_INDIVIDUALS)) {
+    if ((options & TSK_SIMPLIFY_KEEP_UNARY)
+        && (options & TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS)) {
         ret = TSK_ERR_KEEP_UNARY_MUTUALLY_EXCLUSIVE;
         goto out;
     }
diff --git a/c/tskit/tables.h b/c/tskit/tables.h
index 276486efca..43df986e5b 100644
--- a/c/tskit/tables.h
+++ b/c/tskit/tables.h
@@ -696,13 +696,13 @@ typedef struct {
 /**@} */
 
 /* Flags for simplify() */
-#define TSK_FILTER_SITES (1 << 0)
-#define TSK_FILTER_POPULATIONS (1 << 1)
-#define TSK_FILTER_INDIVIDUALS (1 << 2)
-#define TSK_REDUCE_TO_SITE_TOPOLOGY (1 << 3)
-#define TSK_KEEP_UNARY (1 << 4)
-#define TSK_KEEP_INPUT_ROOTS (1 << 5)
-#define TSK_KEEP_UNARY_IN_INDIVIDUALS (1 << 6)
+#define TSK_SIMPLIFY_FILTER_SITES (1 << 0)
+#define TSK_SIMPLIFY_FILTER_POPULATIONS (1 << 1)
+#define TSK_SIMPLIFY_FILTER_INDIVIDUALS (1 << 2)
+#define TSK_SIMPLIFY_REDUCE_TO_SITE_TOPOLOGY (1 << 3)
+#define TSK_SIMPLIFY_KEEP_UNARY (1 << 4)
+#define TSK_SIMPLIFY_KEEP_INPUT_ROOTS (1 << 5)
+#define TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS (1 << 6)
 
 /* Flags for subset() */
 #define TSK_NO_CHANGE_POPULATIONS (1 << 0)
@@ -3859,14 +3859,14 @@ at least ``self->nodes.num_rows`` :c:type:`tsk_id_t` values.
 Options can be specified by providing one or more of the following bitwise
 flags:
 
-TSK_FILTER_SITES
+TSK_SIMPLIFY_FILTER_SITES
     Remove sites from the output if there are no mutations that reference them.
-TSK_FILTER_POPULATIONS
+TSK_SIMPLIFY_FILTER_POPULATIONS
     Remove populations from the output if there are no nodes or migrations that
     reference them.
-TSK_FILTER_INDIVIDUALS
+TSK_SIMPLIFY_FILTER_INDIVIDUALS
     Remove individuals from the output if there are no nodes that reference them.
-TSK_REDUCE_TO_SITE_TOPOLOGY
+TSK_SIMPLIFY_REDUCE_TO_SITE_TOPOLOGY
     Reduce the topological information in the tables to the minimum necessary to
     represent the trees that contain sites. If there are zero sites this will
     result in an zero output edges. When the number of sites is greater than zero,
@@ -3874,16 +3874,16 @@ TSK_REDUCE_TO_SITE_TOPOLOGY
     For a given site, the topology of the tree containing that site will be
     identical (up to node ID remapping) to the topology of the corresponding tree
     in the input.
-TSK_KEEP_UNARY
+TSK_SIMPLIFY_KEEP_UNARY
     By default simplify removes unary nodes (i.e., nodes with exactly one child)
     along the path from samples to root. If this option is specified such unary
     nodes will be preserved in the output.
-TSK_KEEP_INPUT_ROOTS
+TSK_SIMPLIFY_KEEP_INPUT_ROOTS
     By default simplify removes all topology ancestral the MRCAs of the samples.
     This option inserts edges from these MRCAs back to the roots of the input
     trees.
-TSK_KEEP_UNARY_IN_INDIVDUALS
-    This acts like TSK_KEEP_UNARY (and is mutually exclusive with that flag). It
+TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVDUALS
+    This acts like TSK_SIMPLIFY_KEEP_UNARY (and is mutually exclusive with that flag). It
     keeps unary nodes, but only if the unary node is referenced from an individual.
 
 .. note:: Migrations are currently not supported by simplify, and an error will
diff --git a/python/_tskitmodule.c b/python/_tskitmodule.c
index 9a3c332c35..454653afd7 100644
--- a/python/_tskitmodule.c
+++ b/python/_tskitmodule.c
@@ -6573,25 +6573,25 @@ TableCollection_simplify(TableCollection *self, PyObject *args, PyObject *kwds)
     shape = PyArray_DIMS(samples_array);
     num_samples = (tsk_size_t) shape[0];
     if (filter_sites) {
-        options |= TSK_FILTER_SITES;
+        options |= TSK_SIMPLIFY_FILTER_SITES;
     }
     if (filter_individuals) {
-        options |= TSK_FILTER_INDIVIDUALS;
+        options |= TSK_SIMPLIFY_FILTER_INDIVIDUALS;
     }
     if (filter_populations) {
-        options |= TSK_FILTER_POPULATIONS;
+        options |= TSK_SIMPLIFY_FILTER_POPULATIONS;
     }
     if (reduce_to_site_topology) {
-        options |= TSK_REDUCE_TO_SITE_TOPOLOGY;
+        options |= TSK_SIMPLIFY_REDUCE_TO_SITE_TOPOLOGY;
     }
     if (keep_unary) {
-        options |= TSK_KEEP_UNARY;
+        options |= TSK_SIMPLIFY_KEEP_UNARY;
     }
     if (keep_unary_in_individuals) {
-        options |= TSK_KEEP_UNARY_IN_INDIVIDUALS;
+        options |= TSK_SIMPLIFY_KEEP_UNARY_IN_INDIVIDUALS;
     }
     if (keep_input_roots) {
-        options |= TSK_KEEP_INPUT_ROOTS;
+        options |= TSK_SIMPLIFY_KEEP_INPUT_ROOTS;
     }
 
     /* Allocate a new array to hold the node map. */