diff --git a/modules/postgres/postgres.go b/modules/postgres/postgres.go
index cb3d01694b..9feac8b585 100644
--- a/modules/postgres/postgres.go
+++ b/modules/postgres/postgres.go
@@ -3,6 +3,7 @@ package postgres
 import (
 	"context"
 	"fmt"
+	"io"
 	"net"
 	"path/filepath"
 	"strings"
@@ -26,10 +27,9 @@ type PostgresContainer struct {
 	snapshotName string
 }
 
-
 // MustConnectionString panics if the address cannot be determined.
 func (c *PostgresContainer) MustConnectionString(ctx context.Context, args ...string) string {
-	addr, err := c.ConnectionString(ctx,args...)
+	addr, err := c.ConnectionString(ctx, args...)
 	if err != nil {
 		panic(err)
 	}
@@ -185,6 +185,10 @@ func (c *PostgresContainer) Snapshot(ctx context.Context, opts ...SnapshotOption
 		snapshotName = config.snapshotName
 	}
 
+	if c.dbName == "postgres" {
+		return fmt.Errorf("cannot snapshot the postgres system database as it cannot be dropped to be restored")
+	}
+
 	// execute the commands to create the snapshot, in order
 	cmds := []string{
 		// Drop the snapshot database if it already exists
@@ -196,10 +200,19 @@ func (c *PostgresContainer) Snapshot(ctx context.Context, opts ...SnapshotOption
 	}
 
 	for _, cmd := range cmds {
-		_, _, err := c.Exec(ctx, []string{"psql", "-U", c.user, "-c", cmd})
+		exitCode, reader, err := c.Exec(ctx, []string{"psql", "-U", c.user, "-d", c.dbName, "-c", cmd})
 		if err != nil {
 			return err
 		}
+		if exitCode != 0 {
+			buf := new(strings.Builder)
+			_, err := io.Copy(buf, reader)
+			if err != nil {
+				return fmt.Errorf("non-zero exit code for snapshot command, could not read command output: %w", err)
+			}
+
+			return fmt.Errorf("non-zero exit code for snapshot command: %s", buf.String())
+		}
 	}
 
 	c.snapshotName = snapshotName
@@ -220,6 +233,10 @@ func (c *PostgresContainer) Restore(ctx context.Context, opts ...SnapshotOption)
 		snapshotName = config.snapshotName
 	}
 
+	if c.dbName == "postgres" {
+		return fmt.Errorf("cannot restore the postgres system database as it cannot be dropped to be restored")
+	}
+
 	// execute the commands to restore the snapshot, in order
 	cmds := []string{
 		// Drop the entire database by connecting to the postgres global database
@@ -229,10 +246,19 @@ func (c *PostgresContainer) Restore(ctx context.Context, opts ...SnapshotOption)
 	}
 
 	for _, cmd := range cmds {
-		_, _, err := c.Exec(ctx, []string{"psql", "-U", c.user, "-d", "postgres", "-c", cmd})
+		exitCode, reader, err := c.Exec(ctx, []string{"psql", "-v", "ON_ERROR_STOP=1", "-U", c.user, "-d", "postgres", "-c", cmd})
 		if err != nil {
 			return err
 		}
+		if exitCode != 0 {
+			buf := new(strings.Builder)
+			_, err := io.Copy(buf, reader)
+			if err != nil {
+				return fmt.Errorf("non-zero exit code for restore command, could not read command output: %w", err)
+			}
+
+			return fmt.Errorf("non-zero exit code for restore command: %s", buf.String())
+		}
 	}
 
 	return nil
diff --git a/modules/postgres/postgres_test.go b/modules/postgres/postgres_test.go
index 2a74e147f6..9dc2194685 100644
--- a/modules/postgres/postgres_test.go
+++ b/modules/postgres/postgres_test.go
@@ -87,12 +87,12 @@ func TestPostgres(t *testing.T) {
 			connStr, err := container.ConnectionString(ctx, "sslmode=disable", "application_name=test")
 			// }
 			require.NoError(t, err)
-			
-			mustConnStr := container.MustConnectionString(ctx,"sslmode=disable", "application_name=test")
-			if mustConnStr!=connStr{
+
+			mustConnStr := container.MustConnectionString(ctx, "sslmode=disable", "application_name=test")
+			if mustConnStr != connStr {
 				t.Errorf("ConnectionString was not equal to MustConnectionString")
 			}
-				
+
 			// Ensure connection string is using generic format
 			id, err := container.MappedPort(ctx, "5432/tcp")
 			require.NoError(t, err)
@@ -327,3 +327,76 @@ func TestSnapshot(t *testing.T) {
 	})
 	// }
 }
+
+func TestSnapshotWithOverrides(t *testing.T) {
+	ctx := context.Background()
+
+	dbname := "other-db"
+	user := "other-user"
+	password := "other-password"
+
+	container, err := postgres.RunContainer(
+		ctx,
+		testcontainers.WithImage("docker.io/postgres:16-alpine"),
+		postgres.WithDatabase(dbname),
+		postgres.WithUsername(user),
+		postgres.WithPassword(password),
+		testcontainers.WithWaitStrategy(
+			wait.ForLog("database system is ready to accept connections").
+				WithOccurrence(2).
+				WithStartupTimeout(5*time.Second)),
+	)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	_, _, err = container.Exec(ctx, []string{"psql", "-U", user, "-d", dbname, "-c", "CREATE TABLE users (id SERIAL, name TEXT NOT NULL, age INT NOT NULL)"})
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	err = container.Snapshot(ctx, postgres.WithSnapshotName("other-snapshot"))
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	t.Cleanup(func() {
+		if err := container.Terminate(ctx); err != nil {
+			t.Fatalf("failed to terminate container: %s", err)
+		}
+	})
+
+	dbURL, err := container.ConnectionString(ctx)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	t.Run("Test that the restore works when not using defaults", func(t *testing.T) {
+		_, _, err = container.Exec(ctx, []string{"psql", "-U", user, "-d", dbname, "-c", "INSERT INTO users(name, age) VALUES ('test', 42)"})
+		if err != nil {
+			t.Fatal(err)
+		}
+
+		// Doing the restore before we connect since this resets the pgx connection
+		err = container.Restore(ctx)
+		if err != nil {
+			t.Fatal(err)
+		}
+
+		conn, err := pgx.Connect(context.Background(), dbURL)
+		if err != nil {
+			t.Fatal(err)
+		}
+		defer conn.Close(context.Background())
+
+		var count int64
+		err = conn.QueryRow(context.Background(), "SELECT COUNT(1) FROM users").Scan(&count)
+		if err != nil {
+			t.Fatal(err)
+		}
+
+		if count != 0 {
+			t.Fatalf("Expected %d to equal `0`", count)
+		}
+	})
+}