diff --git a/gdb/testsuite/gdb.base/annota1.exp b/gdb/testsuite/gdb.base/annota1.exp
index ac6ad6478f4..42a261e5614 100644
--- a/gdb/testsuite/gdb.base/annota1.exp
+++ b/gdb/testsuite/gdb.base/annota1.exp
@@ -385,6 +385,12 @@ gdb_test_multiple "display value" "set up display" {
     }
 }
 
+# Get the core into the output directory.
+if {![is_remote host]} {
+    gdb_test -prompt "$gdb_prompt$" \
+	"set cwd [file dirname $binfile]" "" \
+	"set inferior cwd to test directory"
+}
 
 # should ask query. Test annotate-query.
 # we don't care about anything else here, only the query.
@@ -479,17 +485,7 @@ if [target_info exists gdb,nosignals] {
 }
 
 # Check for production of a core file and remove it!
-
-set test "cleanup core file"
-if { [remote_file host exists core] } {
-    remote_file host delete core
-    pass "$test (removed)"
-} elseif { $pid != -1 && [remote_file host exists core.$pid] } {
-    remote_file host delete core.$pid
-    pass "$test (removed)"
-} else {
-    pass "$test (not dumped)"
-}
+remove_core $pid
 
 proc thread_test {} {
     global subdir srcdir testfile srcfile binfile
diff --git a/gdb/testsuite/gdb.base/annota3.exp b/gdb/testsuite/gdb.base/annota3.exp
index b747e03718c..4fae6f066ab 100644
--- a/gdb/testsuite/gdb.base/annota3.exp
+++ b/gdb/testsuite/gdb.base/annota3.exp
@@ -273,6 +273,12 @@ gdb_expect_list "set up display" "$gdb_prompt$" {
     "1: value = 7\r\n"
 }
 
+# Get the core into the output directory.
+if {![is_remote host]} {
+    gdb_test -prompt "$gdb_prompt$" \
+	"set cwd [file dirname $binfile]" "" \
+	"set inferior cwd to test directory"
+}
 
 # should ask query. Test annotate-query.
 # we don't care about anything else here, only the query.
@@ -379,17 +385,7 @@ if [target_info exists gdb,nosignals] {
 
 
 # Check for production of a core file and remove it!
-
-set test "cleanup core file"
-if { [remote_file host exists core] } {
-    remote_file host delete core
-    pass "$test (removed)"
-} elseif { $pid != -1 && [remote_file host exists core.$pid] } {
-    remote_file host delete core.$pid
-    pass "$test (removed)"
-} else {
-    pass "$test (not dumped)"
-}
+remove_core $pid
 
 # restore the original prompt for the rest of the testsuite
 
diff --git a/gdb/testsuite/gdb.base/bigcore.exp b/gdb/testsuite/gdb.base/bigcore.exp
index a03a30eca32..13b70f7dd5d 100644
--- a/gdb/testsuite/gdb.base/bigcore.exp
+++ b/gdb/testsuite/gdb.base/bigcore.exp
@@ -53,10 +53,7 @@ gdb_test_no_output "set print sevenbit-strings"
 gdb_test_no_output "set width 0"
 
 # Get the core into the output directory.
-if {![is_remote host]} {
-    gdb_test "cd [file dirname $corefile]" "Working directory .*" \
-	"cd to test directory"
-}
+set_inferior_cwd_to_output_dir
 
 if ![runto_main] then {
     return 0
@@ -116,17 +113,7 @@ gdb_test_no_output "set \$bytes_allocated = bytes_allocated" "save heap size"
 # May 2003) create cores named "core.PID".
 
 # Save the process ID.  Some systems dump the core into core.PID.
-set test "grab pid"
-gdb_test_multiple "info program" $test {
-    -re "child process (\[0-9\]+).*$gdb_prompt $" {
-	set inferior_pid $expect_out(1,string)
-	pass $test
-    }
-    -re "$gdb_prompt $" {
-	set inferior_pid unknown
-	pass $test
-    }
-}
+set inferior_pid [get_inferior_pid]
 
 # Dump core using SIGABRT
 set oldtimeout $timeout
@@ -134,18 +121,11 @@ set timeout 600
 gdb_test "signal SIGABRT" "Program terminated with signal SIGABRT, .*"
 set timeout $oldtimeout
 
-# Find the corefile
-set file ""
-foreach pat [list core.${inferior_pid} ${testfile}.core core] {
-    set names [glob -nocomplain [standard_output_file $pat]]
-    if {[llength $names] == 1} {
-	set file [lindex $names 0]
-	remote_exec build "mv $file $corefile"
-	break
-    }
-}
-
-if { $file == "" } {
+# Find the corefile.
+set file [find_core_file $inferior_pid]
+if { $file != "" } {
+    remote_exec build "mv $file $corefile"
+} else {
     untested "can't generate a core file"
     return 0
 }
@@ -186,9 +166,7 @@ if {! $core_ok} {
 # Now load up that core file
 
 set test "load corefile"
-# We use [file tail] because gdb is still "cd"d to the
-# output directory.
-gdb_test_multiple "core [file tail $corefile]" "$test" {
+gdb_test_multiple "core $corefile" "$test" {
     -re "A program is being debugged already.  Kill it. .y or n. " {
 	send_gdb "y\n"
 	exp_continue
diff --git a/gdb/testsuite/gdb.base/exitsignal.exp b/gdb/testsuite/gdb.base/exitsignal.exp
index 27eb6c5d263..b139bac1be4 100644
--- a/gdb/testsuite/gdb.base/exitsignal.exp
+++ b/gdb/testsuite/gdb.base/exitsignal.exp
@@ -32,11 +32,17 @@ if { [prepare_for_testing "failed to prepare" ${testfile} ${srcfile}] } {
     return -1
 }
 
-# Run to main
+# Run to main.  But, before, change cwd to get the core into the
+# output directory.
+set_inferior_cwd_to_output_dir
+
 if { ![runto_main] } {
     return -1
 }
 
+# Get the inferior's PID for later.
+set pid [get_inferior_pid]
+
 # Print $_exitsignal.  It should be void now, because nothing
 # happened.
 gdb_test "print \$_exitsignal" " = void" \
@@ -53,6 +59,9 @@ gdb_test "continue" "Program received signal SIGSEGV.*" "trigger SIGSEGV"
 gdb_test "continue" "Program terminated with signal SIGSEGV.*" \
     "program terminated with SIGSEGV"
 
+# We don't need the core file, remove it.
+remove_core $pid
+
 # Now, print $_exitsignal again.  It should be 11 (SIGSEGV).
 gdb_test "print \$_exitsignal" " = 11" \
     "\$_exitsignal is 11 (SIGSEGV) after SIGSEGV."
diff --git a/gdb/testsuite/lib/gdb.exp b/gdb/testsuite/lib/gdb.exp
index 4bc5f4f144c..975e861b0f6 100644
--- a/gdb/testsuite/lib/gdb.exp
+++ b/gdb/testsuite/lib/gdb.exp
@@ -7368,6 +7368,88 @@ if {[info exists GDB_PARALLEL]} {
     }
 }
 
+# Set the inferior's cwd to the output directory, in order to have it
+# dump core there.  This must be called before the inferior is
+# started.
+
+proc set_inferior_cwd_to_output_dir {} {
+    # Note this sets the inferior's cwd ("set cwd"), not GDB's ("cd").
+    # If GDB crashes, we want its core dump in gdb/testsuite/, not in
+    # the testcase's dir, so we can detect the unexpected core at the
+    # end of the test run.
+    if {![is_remote host]} {
+	set output_dir [standard_output_file ""]
+	gdb_test_no_output "set cwd $output_dir" \
+	    "set inferior cwd to test directory"
+    }
+}
+
+# Get the inferior's PID.
+
+proc get_inferior_pid {} {
+    set pid -1
+    gdb_test_multiple "inferior" "get inferior pid" {
+	-re "process (\[0-9\]*).*$::gdb_prompt $" {
+	    set pid $expect_out(1,string)
+	    pass $gdb_test_name
+	}
+    }
+    return $pid
+}
+
+# Find the kernel-produced core file dumped for the current testfile
+# program.  PID was the inferior's pid, saved before the inferior
+# exited with a signal, or -1 if not known.  If not on a remote host,
+# this assumes the core was generated in the output directory.
+# Returns the name of the core dump, or empty string if not found.
+
+proc find_core_file {pid} {
+    # For non-remote hosts, since cores are assumed to be in the
+    # output dir, which we control, we use a laxer "core.*" glob.  For
+    # remote hosts, as we don't know whether the dir is being reused
+    # for parallel runs, we use stricter names with no globs.  It is
+    # not clear whether this is really important, but it preserves
+    # status quo ante.
+    set files {}
+    if {![is_remote host]} {
+	lappend files core.*
+    } elseif {$pid != -1} {
+	lappend files core.$pid
+    }
+    lappend files [list ${::testfile}.core core]
+
+    foreach file $files {
+	if {![is_remote host]} {
+	    set names [glob -nocomplain [standard_output_file $file]]
+	    if {[llength $names] == 1} {
+		return [lindex $names 0]
+	    }
+	} else {
+	    if {[remote_file host exists $file]} {
+		return $file
+	    }
+	}
+    }
+    return ""
+}
+
+# Check for production of a core file and remove it.  PID is the
+# inferior's pid or -1 if not known.  TEST is the test's message.
+
+proc remove_core {pid {test ""}} {
+    if {$test == ""} {
+	set test "cleanup core file"
+    }
+
+    set file [find_core_file $pid]
+    if {$file != ""} {
+	remote_file host delete $file
+	pass "$test (removed)"
+    } else {
+	pass "$test (not found)"
+    }
+}
+
 proc core_find {binfile {deletefiles {}} {arg ""}} {
     global objdir subdir
 
@@ -7398,7 +7480,9 @@ proc core_find {binfile {deletefiles {}} {arg ""}} {
 	    set found 1
 	}
     }
-    # Check for "core.PID".
+    # Check for "core.PID", "core.EXEC.PID.HOST.TIME", etc.  It's fine
+    # to use a glob here as we're looking inside a directory we
+    # created.  Also, this procedure only works on non-remote hosts.
     if { $found == 0 } {
 	set names [glob -nocomplain -directory $coredir core.*]
 	if {[llength $names] == 1} {