diff --git a/library/string.m b/library/string.m
index c65e857f8..12bb29177 100644
--- a/library/string.m
+++ b/library/string.m
@@ -1069,19 +1069,26 @@
 :- func rstrip_pred(pred(char)::in(pred(in) is semidet), string::in)
     = (string::out) is det.
 
-    % replace(String0, Search, Replace, String):
+    % replace(String0, Pattern, Subst, String):
     %
-    % Replace replaces the first occurrence of Search in String0
-    % with Replace to give String. It fails if Search does not occur
-    % in String0.
+    % Replaces the first occurrence of Pattern in String0 with Subst to give
+    % String. Fails if Pattern does not occur in String0.
     %
 :- pred replace(string::in, string::in, string::in, string::uo) is semidet.
 
-    % replace_all(String0, Search, Replace, String):
+    % replace_all(String0, Pattern, Subst, String):
     %
-    % Replaces any occurrences of Search in String0 with Replace to give
+    % Replaces any occurrences of Pattern in String0 with Subst to give
     % String.
     %
+    % If Pattern is the empty string then Subst is inserted at every point
+    % in String0 except between two code units in an encoding of a code point.
+    % For example, these are true:
+    %
+    %   replace_all("", "", "|", "|")
+    %   replace_all("a", "", "|", "|a|")
+    %   replace_all("ab", "", "|", "|a|b|")
+    %
 :- func replace_all(string::in, string::in, string::in) = (string::uo) is det.
 :- pred replace_all(string::in, string::in, string::in, string::uo) is det.
 
@@ -4718,10 +4725,7 @@ replace_all(S1, S2, S3) = S4 :-
 
 replace_all(Str, Pat, Subst, Result) :-
     ( if Pat = "" then
-        % XXX ILSEQ foldl cannot handle ill-formed sequences.
-        F = (func(C, L) = [char_to_string(C) ++ Subst | L]),
-        Foldl = foldl(F, Str, []),
-        Result = append_list([Subst | list.reverse(Foldl)])
+        replace_all_empty_pat(Str, Subst, Result)
     else
         PatLength = length(Pat),
         replace_all_loop(Str, Pat, Subst, PatLength, 0, [], ReversedChunks),
@@ -4729,6 +4733,50 @@ replace_all(Str, Pat, Subst, Result) :-
         Result = append_list(Chunks)
     ).
 
+:- pred replace_all_empty_pat(string::in, string::in, string::uo) is det.
+
+replace_all_empty_pat(Str, Subst, Result) :-
+    % This implementation is not the most efficient, but it is not expected
+    % to be used much in practice.
+    to_code_unit_list(Subst, SubstCodes),
+    Codes0 = SubstCodes,
+    replace_all_empty_pat_loop(Str, SubstCodes, length(Str), Codes0, Codes),
+    ( if from_code_unit_list_allow_ill_formed(Codes, ResultPrime) then
+        Result = ResultPrime
+    else
+        unexpected($pred, "string.from_code_unit_list_allow_ill_formed failed")
+    ).
+
+:- pred replace_all_empty_pat_loop(string::in, list(int)::in, int::in,
+    list(int)::in, list(int)::out) is det.
+
+replace_all_empty_pat_loop(Str, Subst, Index, Codes0, Codes) :-
+    ( if unsafe_prev_index(Str, Index, PrevIndex, Char) then
+        char.to_int(Char, CharInt),
+        ( if CharInt =< 0x7f then
+            % Fast path for single code unit code points.
+            Codes1 = [CharInt | Codes0]
+        else
+            prepend_code_units(Str, PrevIndex, Index - 1, Codes0, Codes1)
+        ),
+        Codes2 = Subst ++ Codes1,
+        replace_all_empty_pat_loop(Str, Subst, PrevIndex, Codes2, Codes)
+    else
+        Codes = Codes0
+    ).
+
+:- pred prepend_code_units(string::in, int::in, int::in,
+    list(int)::in, list(int)::out) is det.
+
+prepend_code_units(Str, FirstIndex, Index, Codes0, Codes) :-
+    unsafe_index_code_unit(Str, Index, Code),
+    Codes1 = [Code | Codes0],
+    ( if Index = FirstIndex then
+        Codes = Codes1
+    else
+        prepend_code_units(Str, FirstIndex, Index - 1, Codes1, Codes)
+    ).
+
 :- pred replace_all_loop(string::in, string::in, string::in,
     int::in, int::in, list(string)::in, list(string)::out) is det.
 
diff --git a/tests/general/string_replace.exp b/tests/general/string_replace.exp
index eab49079f..d633a7822 100644
--- a/tests/general/string_replace.exp
+++ b/tests/general/string_replace.exp
@@ -8,6 +8,8 @@ string__replace("aaa bbbb ccccc aaa", "", "**", Result)
 	"**aaa bbbb ccccc aaa"
 string__replace("aßξ啕ßξ啕𐀀.", "", "**", Result) 
 	"**aßξ啕ßξ啕𐀀."
+string__replace("[0x9f][0x98][0x80]😀", "", "**", Result) 
+	"**[0x9f][0x98][0x80]😀"
 string__replace("aaa bbbb ccccc aaa", "aaa", "", Result) 
 	" bbbb ccccc aaa"
 string__replace("aaa bbbb ccccc aaa", "cc", "**", Result) 
@@ -28,6 +30,8 @@ string__replace_all("aaa bbbb ccccc aaa", "", "**", Result)
 	"**a**a**a** **b**b**b**b** **c**c**c**c**c** **a**a**a**"
 string__replace_all("aßξ啕ßξ啕𐀀.", "", "**", Result) 
 	"**a**ß**ξ**啕**ß**ξ**啕**𐀀**.**"
+string__replace_all("[0x9f][0x98][0x80]😀", "", "**", Result) 
+	"**[0x9f]**[0x98]**[0x80]**😀**"
 string__replace_all("aaa bbbb ccccc aaa", "aaa", "", Result) 
 	" bbbb ccccc "
 string__replace_all("aaa bbbb ccccc aaa", "cc", "**", Result) 
diff --git a/tests/general/string_replace.exp2 b/tests/general/string_replace.exp2
new file mode 100644
index 000000000..082aa9237
--- /dev/null
+++ b/tests/general/string_replace.exp2
@@ -0,0 +1,44 @@
+string__replace("", "a", "bc", Result) 
+	FAIL!
+string__replace("aaa bbbb ccccc aaa", "aab", "**", Result) 
+	FAIL!
+string__replace("aaa bbbb ccccc aaa", "aaaa", "**", Result) 
+	FAIL!
+string__replace("aaa bbbb ccccc aaa", "", "**", Result) 
+	"**aaa bbbb ccccc aaa"
+string__replace("aßξ啕ßξ啕𐀀.", "", "**", Result) 
+	"**aßξ啕ßξ啕𐀀."
+string__replace("[0xde00]😀", "", "**", Result) 
+	"**[0xde00]😀"
+string__replace("aaa bbbb ccccc aaa", "aaa", "", Result) 
+	" bbbb ccccc aaa"
+string__replace("aaa bbbb ccccc aaa", "cc", "**", Result) 
+	"aaa bbbb **ccc aaa"
+string__replace("aßξ啕ßξ啕𐀀.", "ßξ", "**", Result) 
+	"a**啕ßξ啕𐀀."
+string__replace("aßξ啕ßξ啕𐀀.", "ßξ", "★★", Result) 
+	"a★★啕ßξ啕𐀀."
+string__replace("aßξ啕ßξ啕𐀀.", "啕ßξ", "***", Result) 
+	"aßξ***啕𐀀."
+string__replace_all("", "a", "bc", Result) 
+	""
+string__replace_all("aaa bbbb ccccc aaa", "aab", "**", Result) 
+	"aaa bbbb ccccc aaa"
+string__replace_all("aaa bbbb ccccc aaa", "aaaa", "**", Result) 
+	"aaa bbbb ccccc aaa"
+string__replace_all("aaa bbbb ccccc aaa", "", "**", Result) 
+	"**a**a**a** **b**b**b**b** **c**c**c**c**c** **a**a**a**"
+string__replace_all("aßξ啕ßξ啕𐀀.", "", "**", Result) 
+	"**a**ß**ξ**啕**ß**ξ**啕**𐀀**.**"
+string__replace_all("[0xde00]😀", "", "**", Result) 
+	"**[0xde00]**😀**"
+string__replace_all("aaa bbbb ccccc aaa", "aaa", "", Result) 
+	" bbbb ccccc "
+string__replace_all("aaa bbbb ccccc aaa", "cc", "**", Result) 
+	"aaa bbbb ****c aaa"
+string__replace_all("aßξ啕ßξ啕𐀀.", "ßξ", "**", Result) 
+	"a**啕**啕𐀀."
+string__replace_all("aßξ啕ßξ啕𐀀.", "ßξ", "★★", Result) 
+	"a★★啕★★啕𐀀."
+string__replace_all("aßξ啕ßξ啕𐀀.", "啕ßξ", "***", Result) 
+	"aßξ***啕𐀀."
diff --git a/tests/general/string_replace.m b/tests/general/string_replace.m
index 2b905fe90..3dcfa2ae8 100644
--- a/tests/general/string_replace.m
+++ b/tests/general/string_replace.m
@@ -1,6 +1,11 @@
 %---------------------------------------------------------------------------%
 % vim: ts=4 sw=4 et ft=mercury
 %---------------------------------------------------------------------------%
+%
+% The .exp file is for backends using UTF-8 string encoding.
+% The .exp2 file is for backends using UTF-16 string encoding.
+%
+%---------------------------------------------------------------------------%
 
 :- module string_replace.
 
@@ -14,6 +19,8 @@
 
 :- implementation.
 
+:- import_module char.
+:- import_module int.
 :- import_module list.
 :- import_module string.
 
@@ -22,6 +29,8 @@
 main(!IO) :-
     Str = "aaa bbbb ccccc aaa",
     Str2 = "aßξ啕ßξ啕𐀀.",
+    Smiley = "😀",
+    Str3 = between(Smiley, 1, length(Smiley)) ++ Smiley,
     Tests = [
         % pattern not in string
         {"", "a", "bc"},
@@ -31,6 +40,7 @@ main(!IO) :-
         % pattern is empty string
         {Str, "", "**"},
         {Str2, "", "**"},
+        {Str3, "", "**"},
 
         % pattern in string
         {Str, "aaa", ""},
@@ -39,31 +49,58 @@ main(!IO) :-
         {Str2, "ßξ", "★★"},
         {Str2, "啕ßξ", "***"}
     ],
-    list__foldl(test_replace, Tests, !IO),
-    list__foldl(test_replace_all, Tests, !IO).
+    list.foldl(test_replace, Tests, !IO),
+    list.foldl(test_replace_all, Tests, !IO).
 
 :- pred test_replace({string, string, string}::in, io::di, io::uo) is det.
 
 test_replace({Str, Pat, Subst}, !IO) :-
-    io__write_string("string__replace(\"" ++ Str ++
-            "\", \"" ++ Pat ++
-            "\", \"" ++ Subst ++ "\", Result) \n\t", !IO),
-    ( string__replace(Str, Pat, Subst, Result) ->
-        io__write(Result, !IO),
-        io__nl(!IO)
-    ;
-        io__write_string("FAIL!\n", !IO)
+    io.write_string("string__replace(\"", !IO),
+    write_string_debug(Str, !IO),
+    io.write_string("\", \"", !IO),
+    io.write_string(Pat, !IO),
+    io.write_string("\", \"", !IO),
+    io.write_string(Subst, !IO),
+    io.write_string("\", Result) \n\t", !IO),
+    ( if string.replace(Str, Pat, Subst, Result) then
+        io.write_string("\"", !IO),
+        write_string_debug(Result, !IO),
+        io.write_string("\"\n", !IO)
+    else
+        io.write_string("FAIL!\n", !IO)
     ).
 
 :- pred test_replace_all({string, string, string}::in, io::di, io::uo) is det.
 
 test_replace_all({Str, Pat, Subst}, !IO) :-
-    io__write_string("string__replace_all(\"" ++ Str ++
-            "\", \"" ++ Pat ++
-            "\", \"" ++ Subst ++ "\", Result) \n\t", !IO),
-    string__replace_all(Str, Pat, Subst, Result),
-    io__write(Result, !IO),
-    io__nl(!IO).
+    io.write_string("string__replace_all(\"", !IO),
+    write_string_debug(Str, !IO),
+    io.write_string("\", \"", !IO),
+    io.write_string(Pat, !IO),
+    io.write_string("\", \"", !IO),
+    io.write_string(Subst, !IO),
+    io.write_string("\", Result) \n\t", !IO),
+    io.write_string("\"", !IO),
+    string.replace_all(Str, Pat, Subst, Result),
+    write_string_debug(Result, !IO),
+    io.write_string("\"\n", !IO).
 
-%---------------------------------------------------------------------------%
-%---------------------------------------------------------------------------%
+:- pred write_string_debug(string::in, io::di, io::uo) is det.
+
+write_string_debug(S, !IO) :-
+    write_string_debug_loop(S, 0, !IO).
+
+:- pred write_string_debug_loop(string::in, int::in, io::di, io::uo) is det.
+
+write_string_debug_loop(S, Index, !IO) :-
+    ( if string.index_next(S, Index, NextIndex, Char) then
+        ( if char.is_surrogate(Char) ; Char = '\ufffd' then
+            unsafe_index_code_unit(S, Index, Code),
+            io.format("[%#x]", [i(Code)], !IO)
+        else
+            io.write_char(Char, !IO)
+        ),
+        write_string_debug_loop(S, NextIndex, !IO)
+    else
+        true
+    ).