diff --git a/pkg/ccl/backupccl/backup_processor.go b/pkg/ccl/backupccl/backup_processor.go
index d9f406132178..8893a7a27de8 100644
--- a/pkg/ccl/backupccl/backup_processor.go
+++ b/pkg/ccl/backupccl/backup_processor.go
@@ -33,6 +33,7 @@ import (
 	"github.com/cockroachdb/cockroach/pkg/sql/sem/builtins"
 	"github.com/cockroachdb/cockroach/pkg/sql/types"
 	"github.com/cockroachdb/cockroach/pkg/storage"
+	"github.com/cockroachdb/cockroach/pkg/util/admission"
 	"github.com/cockroachdb/cockroach/pkg/util/contextutil"
 	"github.com/cockroachdb/cockroach/pkg/util/ctxgroup"
 	"github.com/cockroachdb/cockroach/pkg/util/hlc"
@@ -380,7 +381,15 @@ func runBackupProcessor(
 					// value. The sentinel value of 1 forces the ExportRequest to paginate
 					// after creating a single SST.
 					header.TargetBytes = 1
-
+					admissionHeader := roachpb.AdmissionHeader{
+						// Export requests are currently assigned NormalPri.
+						//
+						// TODO(dt): Consider linking this to/from the UserPriority field.
+						Priority:                 int32(admission.BulkNormalPri),
+						CreateTime:               timeutil.Now().UnixNano(),
+						Source:                   roachpb.AdmissionHeader_FROM_SQL,
+						NoMemoryReservedAtSource: true,
+					}
 					log.Infof(ctx, "sending ExportRequest for span %s (attempt %d, priority %s)",
 						span.span, span.attempts+1, header.UserPriority.String())
 					var rawRes roachpb.Response
@@ -398,8 +407,8 @@ func runBackupProcessor(
 								ReqSentTime: reqSentTime.String(),
 							})
 
-							rawRes, pErr = kv.SendWrappedWith(ctx, flowCtx.Cfg.DB.NonTransactionalSender(),
-								header, req)
+							rawRes, pErr = kv.SendWrappedWithAdmission(ctx, flowCtx.Cfg.DB.NonTransactionalSender(),
+								header, admissionHeader, req)
 							respReceivedTime = timeutil.Now()
 							if pErr != nil {
 								return pErr.GoError()
diff --git a/pkg/kv/sender.go b/pkg/kv/sender.go
index 9ab8e2e1ce44..607b7369c829 100644
--- a/pkg/kv/sender.go
+++ b/pkg/kv/sender.go
@@ -428,9 +428,24 @@ func (f NonTransactionalFactoryFunc) NonTransactionalSender() Sender {
 // `nil` context; an empty one is used in that case.
 func SendWrappedWith(
 	ctx context.Context, sender Sender, h roachpb.Header, args roachpb.Request,
+) (roachpb.Response, *roachpb.Error) {
+	return SendWrappedWithAdmission(ctx, sender, h, roachpb.AdmissionHeader{}, args)
+}
+
+// SendWrappedWithAdmission is a convenience function which wraps the request
+// in a batch and sends it via the provided Sender and headers. It returns the
+// unwrapped response or an error. It's valid to pass a `nil` context; an
+// empty one is used in that case.
+func SendWrappedWithAdmission(
+	ctx context.Context,
+	sender Sender,
+	h roachpb.Header,
+	ah roachpb.AdmissionHeader,
+	args roachpb.Request,
 ) (roachpb.Response, *roachpb.Error) {
 	ba := roachpb.BatchRequest{}
 	ba.Header = h
+	ba.AdmissionHeader = ah
 	ba.Add(args)
 
 	br, pErr := sender.Send(ctx, ba)
diff --git a/pkg/util/admission/work_queue.go b/pkg/util/admission/work_queue.go
index 6e44ec546385..06e25cfe230b 100644
--- a/pkg/util/admission/work_queue.go
+++ b/pkg/util/admission/work_queue.go
@@ -68,6 +68,9 @@ type WorkPriority int8
 const (
 	// LowPri is low priority work.
 	LowPri WorkPriority = math.MinInt8
+	// BulkNormalPri is bulk priority work from bulk jobs, which could be run due
+	// to user submissions or be automatic.
+	BulkNormalPri WorkPriority = -30
 	// NormalPri is normal priority work.
 	NormalPri WorkPriority = 0
 	// HighPri is high priority work.