diff --git a/Makefile b/Makefile
index 4edfda3e00..42a7ed96e2 100644
--- a/Makefile
+++ b/Makefile
@@ -722,6 +722,7 @@ TEST_BUILTINS_OBJS += test-online-cpus.o
 TEST_BUILTINS_OBJS += test-parse-options.o
 TEST_BUILTINS_OBJS += test-parse-pathspec-file.o
 TEST_BUILTINS_OBJS += test-path-utils.o
+TEST_BUILTINS_OBJS += test-pcre2-config.o
 TEST_BUILTINS_OBJS += test-pkt-line.o
 TEST_BUILTINS_OBJS += test-prio-queue.o
 TEST_BUILTINS_OBJS += test-proc-receive.o
diff --git a/grep.c b/grep.c
index 242b4a3506..305c579aff 100644
--- a/grep.c
+++ b/grep.c
@@ -493,7 +493,13 @@ static void compile_pcre2_pattern(struct grep_pat *p, const struct grep_opt *opt
 	}
 	if (!opt->ignore_locale && is_utf8_locale() && has_non_ascii(p->pattern) &&
 	    (opt->ignore_case || !fixed))
-		options |= PCRE2_UTF;
+		options |= (PCRE2_UTF | PCRE2_MATCH_INVALID_UTF);
+
+	if (PCRE2_MATCH_INVALID_UTF &&
+	    options & (PCRE2_UTF | PCRE2_CASELESS) &&
+	    !(PCRE2_MAJOR >= 10 && PCRE2_MAJOR >= 36))
+		/* Work around https://bugs.exim.org/show_bug.cgi?id=2642 fixed in 10.36 */
+		options |= PCRE2_NO_START_OPTIMIZE;
 
 	p->pcre2_pattern = pcre2_compile((PCRE2_SPTR)p->pattern,
 					 p->patternlen, options, &error, &erroffset,
diff --git a/grep.h b/grep.h
index b5c4e223a8..ade21c8812 100644
--- a/grep.h
+++ b/grep.h
@@ -18,6 +18,10 @@ typedef int pcre2_code;
 typedef int pcre2_match_data;
 typedef int pcre2_compile_context;
 #endif
+#ifndef PCRE2_MATCH_INVALID_UTF
+/* PCRE2_MATCH_* dummy also with !USE_LIBPCRE2, for test-pcre2-config.c */
+#define PCRE2_MATCH_INVALID_UTF 0
+#endif
 #include "thread-utils.h"
 #include "userdiff.h"
 
diff --git a/t/helper/test-pcre2-config.c b/t/helper/test-pcre2-config.c
new file mode 100644
index 0000000000..5258fdddba
--- /dev/null
+++ b/t/helper/test-pcre2-config.c
@@ -0,0 +1,12 @@
+#include "test-tool.h"
+#include "cache.h"
+#include "grep.h"
+
+int cmd__pcre2_config(int argc, const char **argv)
+{
+	if (argc == 2 && !strcmp(argv[1], "has-PCRE2_MATCH_INVALID_UTF")) {
+		int value = PCRE2_MATCH_INVALID_UTF;
+		return !value;
+	}
+	return 1;
+}
diff --git a/t/helper/test-tool.c b/t/helper/test-tool.c
index 9d6d14d929..f97cd9f48a 100644
--- a/t/helper/test-tool.c
+++ b/t/helper/test-tool.c
@@ -46,6 +46,7 @@ static struct test_cmd cmds[] = {
 	{ "parse-options", cmd__parse_options },
 	{ "parse-pathspec-file", cmd__parse_pathspec_file },
 	{ "path-utils", cmd__path_utils },
+	{ "pcre2-config", cmd__pcre2_config },
 	{ "pkt-line", cmd__pkt_line },
 	{ "prio-queue", cmd__prio_queue },
 	{ "proc-receive", cmd__proc_receive},
diff --git a/t/helper/test-tool.h b/t/helper/test-tool.h
index a6470ff62c..28072c0ad5 100644
--- a/t/helper/test-tool.h
+++ b/t/helper/test-tool.h
@@ -35,6 +35,7 @@ int cmd__online_cpus(int argc, const char **argv);
 int cmd__parse_options(int argc, const char **argv);
 int cmd__parse_pathspec_file(int argc, const char** argv);
 int cmd__path_utils(int argc, const char **argv);
+int cmd__pcre2_config(int argc, const char **argv);
 int cmd__pkt_line(int argc, const char **argv);
 int cmd__prio_queue(int argc, const char **argv);
 int cmd__proc_receive(int argc, const char **argv);
diff --git a/t/t7812-grep-icase-non-ascii.sh b/t/t7812-grep-icase-non-ascii.sh
index 38457c2e4f..e5d1e4ea68 100755
--- a/t/t7812-grep-icase-non-ascii.sh
+++ b/t/t7812-grep-icase-non-ascii.sh
@@ -57,7 +57,12 @@ test_expect_success GETTEXT_LOCALE,LIBPCRE2 'PCRE v2: setup invalid UTF-8 data'
 	printf "\\200\\n" >invalid-0x80 &&
 	echo "ævar" >expected &&
 	cat expected >>invalid-0x80 &&
-	git add invalid-0x80
+	git add invalid-0x80 &&
+
+	# Test for PCRE2_MATCH_INVALID_UTF bug
+	# https://bugs.exim.org/show_bug.cgi?id=2642
+	printf "\\345Aæ\\n" >invalid-0xe5 &&
+	git add invalid-0xe5
 '
 
 test_expect_success GETTEXT_LOCALE,LIBPCRE2 'PCRE v2: grep ASCII from invalid UTF-8 data' '
@@ -67,6 +72,13 @@ test_expect_success GETTEXT_LOCALE,LIBPCRE2 'PCRE v2: grep ASCII from invalid UT
 	test_cmp expected actual
 '
 
+test_expect_success GETTEXT_LOCALE,LIBPCRE2 'PCRE v2: grep ASCII from invalid UTF-8 data (PCRE2 bug #2642)' '
+	git grep -h "Aæ" invalid-0xe5 >actual &&
+	test_cmp invalid-0xe5 actual &&
+	git grep -h "(*NO_JIT)Aæ" invalid-0xe5 >actual &&
+	test_cmp invalid-0xe5 actual
+'
+
 test_expect_success GETTEXT_LOCALE,LIBPCRE2 'PCRE v2: grep non-ASCII from invalid UTF-8 data' '
 	git grep -h "æ" invalid-0x80 >actual &&
 	test_cmp expected actual &&
@@ -74,9 +86,41 @@ test_expect_success GETTEXT_LOCALE,LIBPCRE2 'PCRE v2: grep non-ASCII from invali
 	test_cmp expected actual
 '
 
+test_expect_success GETTEXT_LOCALE,LIBPCRE2 'PCRE v2: grep non-ASCII from invalid UTF-8 data (PCRE2 bug #2642)' '
+	git grep -h "Aæ" invalid-0xe5 >actual &&
+	test_cmp invalid-0xe5 actual &&
+	git grep -h "(*NO_JIT)Aæ" invalid-0xe5 >actual &&
+	test_cmp invalid-0xe5 actual
+'
+
+test_lazy_prereq PCRE2_MATCH_INVALID_UTF '
+	test-tool pcre2-config has-PCRE2_MATCH_INVALID_UTF
+'
+
 test_expect_success GETTEXT_LOCALE,LIBPCRE2 'PCRE v2: grep non-ASCII from invalid UTF-8 data with -i' '
 	test_might_fail git grep -hi "Æ" invalid-0x80 >actual &&
 	test_might_fail git grep -hi "(*NO_JIT)Æ" invalid-0x80 >actual
 '
 
+test_expect_success GETTEXT_LOCALE,LIBPCRE2,PCRE2_MATCH_INVALID_UTF 'PCRE v2: grep non-ASCII from invalid UTF-8 data with -i' '
+	git grep -hi "Æ" invalid-0x80 >actual &&
+	test_cmp expected actual &&
+	git grep -hi "(*NO_JIT)Æ" invalid-0x80 >actual &&
+	test_cmp expected actual
+'
+
+test_expect_success GETTEXT_LOCALE,LIBPCRE2,PCRE2_MATCH_INVALID_UTF 'PCRE v2: grep non-ASCII from invalid UTF-8 data with -i (PCRE2 bug #2642)' '
+	git grep -hi "Æ" invalid-0xe5 >actual &&
+	test_cmp invalid-0xe5 actual &&
+	git grep -hi "(*NO_JIT)Æ" invalid-0xe5 >actual &&
+	test_cmp invalid-0xe5 actual &&
+
+	# Only the case of grepping the ASCII part in a way that
+	# relies on -i fails
+	git grep -hi "aÆ" invalid-0xe5 >actual &&
+	test_cmp invalid-0xe5 actual &&
+	git grep -hi "(*NO_JIT)aÆ" invalid-0xe5 >actual &&
+	test_cmp invalid-0xe5 actual
+'
+
 test_done
