diff --git a/t/56_open_flags.t b/t/56_open_flags.t
index 5bb08df..ea4e3e3 100644
--- a/t/56_open_flags.t
+++ b/t/56_open_flags.t
@@ -11,7 +11,7 @@ use Test::More tests => 8;
 use DBI;
 use DBD::SQLite;
 
-my $dbfile = 'foo';
+my $dbfile = dbfile('foo');
 unlink $dbfile if -f $dbfile;
 
 {
diff --git a/t/57_uri_filename.t b/t/57_uri_filename.t
index 45eec76..8923a6c 100644
--- a/t/57_uri_filename.t
+++ b/t/57_uri_filename.t
@@ -11,12 +11,12 @@ use Test::More tests => 17;
 use DBI;
 use DBD::SQLite;
 
-my $dbfile = 'foo';
+my $dbfile = dbfile('foo');
 my %uri = (
-  base => 'file:foo',
-  ro   => 'file:foo?mode=ro',
-  rw   => 'file:foo?mode=rw',
-  rwc  => 'file:foo?mode=rwc',
+  base => "file:$dbfile",
+  ro   => "file:$dbfile?mode=ro",
+  rw   => "file:$dbfile?mode=rw",
+  rwc  => "file:$dbfile?mode=rwc",
 );
 
 sub cleanup {
diff --git a/t/lib/Test.pm b/t/lib/Test.pm
index 9376fd4..3de22c5 100644
--- a/t/lib/Test.pm
+++ b/t/lib/Test.pm
@@ -25,7 +25,7 @@ BEGIN {
 # Always load the DBI module
 use DBI ();
 
-sub dbfile { $dbfiles{$_[0]} }
+sub dbfile { $dbfiles{$_[0]} ||= (defined $_[0] && length $_[0] && $_[0] ne ':memory:') ? $_[0] . $$ : $_[0] }
 
 # Delete temporary files
 sub clean {
@@ -47,9 +47,8 @@ END   { clean() }
 # A simplified connect function for the most common case
 sub connect_ok {
 	my $attr = { @_ };
-	my $dbfile = defined $attr->{dbfile} ? delete $attr->{dbfile} : ':memory:';
-	$dbfiles{$dbfile} = (defined $dbfile && length $dbfile && $dbfile ne ':memory:') ? $dbfile . $$ : $dbfile;
-	my @params = ( "dbi:SQLite:dbname=$dbfiles{$dbfile}", '', '' );
+	my $dbfile = dbfile(defined $attr->{dbfile} ? delete $attr->{dbfile} : ':memory:');
+	my @params = ( "dbi:SQLite:dbname=$dbfile", '', '' );
 	if ( %$attr ) {
 		push @params, $attr;
 	}