diff --git a/fs/accounting/accounting.go b/fs/accounting/accounting.go
index 34850b5c5..105c72a20 100644
--- a/fs/accounting/accounting.go
+++ b/fs/accounting/accounting.go
@@ -280,6 +280,12 @@ func (acc *Account) ServerSideCopyEnd(n int64) {
 	acc.stats.Bytes(n)
 }
 
+// DryRun accounts for statistics without running the operation
+func (acc *Account) DryRun(n int64) {
+	acc.ServerSideCopyStart()
+	acc.ServerSideCopyEnd(n)
+}
+
 // Account for n bytes from the current file bandwidth limit (if any)
 func (acc *Account) limitPerFileBandwidth(n int) {
 	acc.values.mu.Lock()
diff --git a/fs/operations/operations.go b/fs/operations/operations.go
index 8f6415965..39358aaa4 100644
--- a/fs/operations/operations.go
+++ b/fs/operations/operations.go
@@ -368,6 +368,8 @@ func Copy(ctx context.Context, f fs.Fs, dst fs.Object, remote string, src fs.Obj
 	}()
 	newDst = dst
 	if SkipDestructive(ctx, src, "copy") {
+		in := tr.Account(ctx, nil)
+		in.DryRun(src.Size())
 		return newDst, nil
 	}
 	maxTries := ci.LowLevelRetries
@@ -559,6 +561,8 @@ func Move(ctx context.Context, fdst fs.Fs, dst fs.Object, remote string, src fs.
 	}()
 	newDst = dst
 	if SkipDestructive(ctx, src, "move") {
+		in := tr.Account(ctx, nil)
+		in.DryRun(src.Size())
 		return newDst, nil
 	}
 	// See if we have Move available
@@ -1929,6 +1933,12 @@ func (l *ListFormat) Format(entry *ListJSONItem) (result string) {
 // if available) and doing renames in parallel.
 func DirMove(ctx context.Context, f fs.Fs, srcRemote, dstRemote string) (err error) {
 	ci := fs.GetConfig(ctx)
+
+	if SkipDestructive(ctx, srcRemote, "dirMove") {
+		accounting.Stats(ctx).Renames(1)
+		return nil
+	}
+
 	// Use DirMove if possible
 	if doDirMove := f.Features().DirMove; doDirMove != nil {
 		err = doDirMove(ctx, f, srcRemote, dstRemote)