diff --git a/testing/btest/Baseline/language.set/out b/testing/btest/Baseline/language.set/out
index fa52244f6d..f055d1dd03 100644
--- a/testing/btest/Baseline/language.set/out
+++ b/testing/btest/Baseline/language.set/out
@@ -70,3 +70,8 @@ equality (FAIL)
 non-equality (PASS)
 equality (FAIL)
 magnitude (FAIL)
+nested-set-add (PASS)
+nested-set-add (PASS)
+nested-set-add (PASS)
+nested-set-del (PASS)
+nested-set-in (PASS)
diff --git a/testing/btest/Baseline/language.table-nested-set-ordering/out b/testing/btest/Baseline/language.table-nested-set-ordering/out
new file mode 100644
index 0000000000..5f99ba9e93
--- /dev/null
+++ b/testing/btest/Baseline/language.table-nested-set-ordering/out
@@ -0,0 +1,5 @@
+### BTest baseline data generated by btest-diff. Do not edit. Use "btest -U/-u" to update. Requires BTest >= 0.63.
+[a={
+SHA1,
+MD5
+}, b=12345678901234567890, c=<uninitialized>]
diff --git a/testing/btest/Baseline/language.table/out b/testing/btest/Baseline/language.table/out
index a0e5ab114d..e637e81437 100644
--- a/testing/btest/Baseline/language.table/out
+++ b/testing/btest/Baseline/language.table/out
@@ -47,3 +47,5 @@ remove element (PASS)
 !in operator (PASS)
 remove element (PASS)
 !in operator (PASS)
+nested table addition (PASS)
+nested table removal (PASS)
diff --git a/testing/btest/language/nested-sets.zeek b/testing/btest/language/nested-sets.zeek
index 1e83b6184d..35d2275a61 100644
--- a/testing/btest/language/nested-sets.zeek
+++ b/testing/btest/language/nested-sets.zeek
@@ -28,6 +28,8 @@ type r: record {
 	b: set[count];
 };
 
+type s: set[set[count]];
+
 global foo: set[r];
 global bar = set(1,3,5);
 
diff --git a/testing/btest/language/set.zeek b/testing/btest/language/set.zeek
index 1c3ab85ef2..847d4ad4bc 100644
--- a/testing/btest/language/set.zeek
+++ b/testing/btest/language/set.zeek
@@ -24,6 +24,7 @@ event zeek_init()
 	local s6: set[port, string, bool] = set();
 	local s7: set[port, string, bool];
 	local s8 = set( [8/tcp, "type inference", T] );
+	local s9: set[set[count]] = set();
 
 	# Type inference tests
 
@@ -181,5 +182,15 @@ event zeek_init()
 	test_case( "equality", a == a | set(5,11) );
 
 	test_case( "magnitude", |a_and_b| == |a_or_b|);
+
+	add s9[set(1,2,3)];
+	test_case( "nested-set-add", |s9| == 1 );
+	add s9[set(1,2,3)];
+	test_case( "nested-set-add", |s9| == 1 );
+	add s9[set(2,3,4)];
+	test_case( "nested-set-add", |s9| == 2 );
+	delete s9[set(1,2,3)];
+	test_case( "nested-set-del", |s9| == 1 );
+	test_case( "nested-set-in", set(2,3,4) in s9 );
 }
 
diff --git a/testing/btest/language/table-nested-set-ordering.zeek b/testing/btest/language/table-nested-set-ordering.zeek
new file mode 100644
index 0000000000..83a3ae8f68
--- /dev/null
+++ b/testing/btest/language/table-nested-set-ordering.zeek
@@ -0,0 +1,25 @@
+# This testcase used to cause subtle memory overflow problems due to deviating
+# traversal order of the k$a set members. With 4.2, this will trigger an
+# InternalError due to new bounds-checking. For context, see GHI-1753.
+#
+# @TEST-EXEC: zeek -b %INPUT >out
+# @TEST-EXEC: btest-diff out
+
+type Key: record {
+  a: set[string];
+  b: string &optional;
+  c: string &optional;
+};
+
+global state: table[Key] of count = {};
+
+event zeek_init() {
+
+  local k: Key;
+
+  k$a = set("MD5", "SHA1");
+  k$b = "12345678901234567890";
+
+  state[k] = 1;
+  print k;
+}
diff --git a/testing/btest/language/table.zeek b/testing/btest/language/table.zeek
index cb26b5c17b..92284986ec 100644
--- a/testing/btest/language/table.zeek
+++ b/testing/btest/language/table.zeek
@@ -29,6 +29,9 @@ event zeek_init()
 	local t11: table[conn_id, bool] of count = {
 	    [ [$orig_h=1.1.1.1, $orig_p=1234/tcp,
 	       $resp_h=2.2.2.2, $resp_p=4321/tcp], T ] = 42 };
+	local t12: table[table[count] of string] of string = {
+		[table([1] = "foo", [2] = "bar")] = "oh1"
+	};
 
 	# Type inference tests
 
@@ -159,5 +162,10 @@ event zeek_init()
 	delete t11[cid, T];
 	test_case( "remove element", |t11| == 1 );
 	test_case( "!in operator", [cid, T] !in t11 );
+
+	t12[table([2] = "blum", [3] = "frub")] = "oh2";
+	test_case( "nested table addition", |t12| == 2 );
+	delete t12[table([1] = "foo", [2] = "bar")];
+	test_case( "nested table removal", |t12| == 1 );
 }