diff --git a/pgconn/pgconn.go b/pgconn/pgconn.go
index 478711245..768d3e710 100644
--- a/pgconn/pgconn.go
+++ b/pgconn/pgconn.go
@@ -13,6 +13,7 @@ import (
 	"net"
 	"strconv"
 	"strings"
+	"sync"
 	"time"
 
 	"github.com/jackc/pgx/v5/internal/iobufpool"
@@ -75,6 +76,11 @@ type PgConn struct {
 
 	status byte // One of connStatus* constants
 
+	bufferingReceive    bool
+	bufferingReceiveMux sync.Mutex
+	bufferingReceiveMsg pgproto3.BackendMessage
+	bufferingReceiveErr error
+
 	peekedMsg pgproto3.BackendMessage
 
 	// Reusable / preallocated resources
@@ -419,6 +425,24 @@ func hexMD5(s string) string {
 	return hex.EncodeToString(hash.Sum(nil))
 }
 
+func (pgConn *PgConn) signalMessage() chan struct{} {
+	if pgConn.bufferingReceive {
+		panic("BUG: signalMessage when already in progress")
+	}
+
+	pgConn.bufferingReceive = true
+	pgConn.bufferingReceiveMux.Lock()
+
+	ch := make(chan struct{})
+	go func() {
+		pgConn.bufferingReceiveMsg, pgConn.bufferingReceiveErr = pgConn.frontend.Receive()
+		pgConn.bufferingReceiveMux.Unlock()
+		close(ch)
+	}()
+
+	return ch
+}
+
 // ReceiveMessage receives one wire protocol message from the PostgreSQL server. It must only be used when the
 // connection is not busy. e.g. It is an error to call ReceiveMessage while reading the result of a query. The messages
 // are still handled by the core pgconn message handling system so receiving a NotificationResponse will still trigger
@@ -458,7 +482,23 @@ func (pgConn *PgConn) peekMessage() (pgproto3.BackendMessage, error) {
 		return pgConn.peekedMsg, nil
 	}
 
-	msg, err := pgConn.frontend.Receive()
+	var msg pgproto3.BackendMessage
+	var err error
+	if pgConn.bufferingReceive {
+		pgConn.bufferingReceiveMux.Lock()
+		msg = pgConn.bufferingReceiveMsg
+		err = pgConn.bufferingReceiveErr
+		pgConn.bufferingReceiveMux.Unlock()
+		pgConn.bufferingReceive = false
+
+		// If a timeout error happened in the background try the read again.
+		var netErr net.Error
+		if errors.As(err, &netErr) && netErr.Timeout() {
+			msg, err = pgConn.frontend.Receive()
+		}
+	} else {
+		msg, err = pgConn.frontend.Receive()
+	}
 
 	if err != nil {
 		// Close on anything other than timeout error - everything else is fatal
@@ -1155,7 +1195,7 @@ func (pgConn *PgConn) CopyFrom(ctx context.Context, r io.Reader, sql string) (Co
 		defer pgConn.contextWatcher.Unwatch()
 	}
 
-	// Send copy to command
+	// Send copy from query
 	pgConn.frontend.SendQuery(&pgproto3.Query{String: sql})
 	err := pgConn.frontend.Flush()
 	if err != nil {
@@ -1163,52 +1203,55 @@ func (pgConn *PgConn) CopyFrom(ctx context.Context, r io.Reader, sql string) (Co
 		return CommandTag{}, err
 	}
 
-	// err = pgConn.conn.SetReadDeadline(nbconn.NonBlockingDeadline)
-	// if err != nil {
-	// 	pgConn.asyncClose()
-	// 	return CommandTag{}, err
-	// }
-	nonblocking := true
-	defer func() {
-		if nonblocking {
-			pgConn.conn.SetReadDeadline(time.Time{})
-		}
-	}()
-
-	buf := iobufpool.Get(65536)
-	defer iobufpool.Put(buf)
-	(*buf)[0] = 'd'
+	// Send copy data
+	abortCopyChan := make(chan struct{})
+	copyErrChan := make(chan error, 1)
+	signalMessageChan := pgConn.signalMessage()
+	var wg sync.WaitGroup
+	wg.Add(1)
 
-	var readErr, pgErr error
-	for pgErr == nil {
-		// Read chunk from r.
-		var n int
-		n, readErr = r.Read((*buf)[5:cap(*buf)])
+	go func() {
+		defer wg.Done()
+		buf := iobufpool.Get(65536)
+		defer iobufpool.Put(buf)
+		(*buf)[0] = 'd'
 
-		// Send chunk to PostgreSQL.
-		if n > 0 {
-			*buf = (*buf)[0 : n+5]
-			pgio.SetInt32((*buf)[1:], int32(n+4))
+		for {
+			n, readErr := r.Read((*buf)[5:cap(*buf)])
+			if n > 0 {
+				*buf = (*buf)[0 : n+5]
+				pgio.SetInt32((*buf)[1:], int32(n+4))
+
+				writeErr := pgConn.frontend.SendUnbufferedEncodedCopyData(*buf)
+				if writeErr != nil {
+					// Write errors are always fatal, but we can't use asyncClose because we are in a different goroutine.
+					pgConn.conn.Close()
 
-			writeErr := pgConn.frontend.SendUnbufferedEncodedCopyData(*buf)
-			if writeErr != nil {
-				pgConn.asyncClose()
-				return CommandTag{}, err
+					copyErrChan <- writeErr
+					return
+				}
+			}
+			if readErr != nil {
+				copyErrChan <- readErr
+				return
 			}
-		}
 
-		// Abort loop if there was a read error.
-		if readErr != nil {
-			break
+			select {
+			case <-abortCopyChan:
+				return
+			default:
+			}
 		}
+	}()
 
-		// Read messages until error or none available.
-		for pgErr == nil {
+	var pgErr error
+	var copyErr error
+	for copyErr == nil && pgErr == nil {
+		select {
+		case copyErr = <-copyErrChan:
+		case <-signalMessageChan:
 			msg, err := pgConn.receiveMessage()
 			if err != nil {
-				// if errors.Is(err, nbconn.ErrWouldBlock) {
-				// 	break
-				// }
 				pgConn.asyncClose()
 				return CommandTag{}, normalizeTimeoutError(ctx, err)
 			}
@@ -1216,22 +1259,19 @@ func (pgConn *PgConn) CopyFrom(ctx context.Context, r io.Reader, sql string) (Co
 			switch msg := msg.(type) {
 			case *pgproto3.ErrorResponse:
 				pgErr = ErrorResponseToPgError(msg)
-				break
+			default:
+				signalMessageChan = pgConn.signalMessage()
 			}
 		}
 	}
+	close(abortCopyChan)
+	// Make sure io goroutine finishes before writing.
+	wg.Wait()
 
-	err = pgConn.conn.SetReadDeadline(time.Time{})
-	if err != nil {
-		pgConn.asyncClose()
-		return CommandTag{}, err
-	}
-	nonblocking = false
-
-	if readErr == io.EOF || pgErr != nil {
+	if copyErr == io.EOF || pgErr != nil {
 		pgConn.frontend.Send(&pgproto3.CopyDone{})
 	} else {
-		pgConn.frontend.Send(&pgproto3.CopyFail{Message: readErr.Error()})
+		pgConn.frontend.Send(&pgproto3.CopyFail{Message: copyErr.Error()})
 	}
 	err = pgConn.frontend.Flush()
 	if err != nil {