diff --git a/development/PAINTING_ANALYSIS b/development/PAINTING_ANALYSIS
index beb0fad4f6..e4efe84414 100644
--- a/development/PAINTING_ANALYSIS
+++ b/development/PAINTING_ANALYSIS
@@ -123,6 +123,11 @@ In particular, if text is painted last, it will be more visible in the
 presence of underlines (foreign language, change tracking, spell
 check).
 
+** DONE remove pit argument to breakRow
+
+There are probably other places where the pit is not needed anymore:
+computeRowMetrics, labelFill, setRowHeight, isLastRow, isFirstRow
+
 ** Remember rtl status in the row object
 
 This will avoid to pass a Paragraph object to methods that do not need it.
diff --git a/src/BufferView.cpp b/src/BufferView.cpp
index 9708a08aeb..2739e00ba3 100644
--- a/src/BufferView.cpp
+++ b/src/BufferView.cpp
@@ -2999,8 +2999,7 @@ void BufferView::checkCursorScrollOffset(PainterInfo & pi)
 		bool const drawing = pi.pain.isDrawingEnabled();
 		pi.pain.setDrawingEnabled(false);
 		// No need to care about vertical position.
-		RowPainter rp(pi, buffer().text(), d->cursor_.bottom().pit(), row,
-		              -d->horiz_scroll_offset_, 0);
+		RowPainter rp(pi, buffer().text(), row, -d->horiz_scroll_offset_, 0);
 		rp.paintText();
 		pi.pain.setDrawingEnabled(drawing);
 	}
diff --git a/src/RowPainter.cpp b/src/RowPainter.cpp
index 1c2b65dfab..a2ff309347 100644
--- a/src/RowPainter.cpp
+++ b/src/RowPainter.cpp
@@ -54,12 +54,12 @@ using frontend::FontMetrics;
 
 
 RowPainter::RowPainter(PainterInfo & pi,
-	Text const & text, pit_type pit, Row const & row, int x, int y)
+	Text const & text, Row const & row, int x, int y)
 	: pi_(pi), text_(text),
 	  text_metrics_(pi_.base.bv->textMetrics(&text)),
 	  pars_(text.paragraphs()),
-	  row_(row), pit_(pit), par_(text.paragraphs()[pit]),
-	  pm_(text_metrics_.parMetrics(pit)), change_(pi_.change_),
+	  row_(row), par_(text.paragraphs()[row.pit()]),
+	  pm_(text_metrics_.parMetrics(row.pit())), change_(pi_.change_),
 	  xo_(x), yo_(y), width_(text_metrics_.width()),
 	  solid_line_thickness_(1), solid_line_offset_(1),
 	  dotted_line_thickness_(1)
@@ -84,8 +84,8 @@ RowPainter::RowPainter(PainterInfo & pi,
 	//lyxerr << "RowPainter: x: " << x_ << " xo: " << xo_ << " yo: " << yo_ << endl;
 	//row_.dump();
 
-	LBUFERR(pit >= 0);
-	LBUFERR(pit < int(text.paragraphs().size()));
+	LBUFERR(row.pit() >= 0);
+	LBUFERR(row.pit() < int(text.paragraphs().size()));
 }
 
 
@@ -280,7 +280,7 @@ void RowPainter::paintChangeBar() const
 	if (start == end || !par_.isChanged(start, end))
 		return;
 
-	int const height = text_metrics_.isLastRow(pit_, row_)
+	int const height = text_metrics_.isLastRow(row_)
 		? row_.ascent()
 		: row_.height();
 
@@ -312,16 +312,16 @@ void RowPainter::paintDepthBar() const
 		return;
 
 	depth_type prev_depth = 0;
-	if (!text_metrics_.isFirstRow(pit_, row_)) {
-		pit_type pit2 = pit_;
+	if (!text_metrics_.isFirstRow(row_)) {
+		pit_type pit2 = row_.pit();
 		if (row_.pos() == 0)
 			--pit2;
 		prev_depth = pars_[pit2].getDepth();
 	}
 
 	depth_type next_depth = 0;
-	if (!text_metrics_.isLastRow(pit_, row_)) {
-		pit_type pit2 = pit_;
+	if (!text_metrics_.isLastRow(row_)) {
+		pit_type pit2 = row_.pit();
 		if (row_.endpos() >= pars_[pit2].size())
 			++pit2;
 		next_depth = pars_[pit2].getDepth();
@@ -396,7 +396,7 @@ void RowPainter::paintFirst() const
 	    paintAppendixStart(yo_ - row_.ascent() + 2 * defaultRowHeight());
 
 	bool const is_first =
-		text_.isFirstInSequence(pit_) || !layout.isParagraphGroup();
+		text_.isFirstInSequence(row_.pit()) || !layout.isParagraphGroup();
 	//lyxerr << "paintFirst: " << par_.id() << " is_seq: " << is_seq << endl;
 
 	if (layout.labelIsInline()
@@ -500,7 +500,7 @@ static int getEndLabel(pit_type p, Text const & text)
 void RowPainter::paintLast() const
 {
 	bool const is_rtl = text_.isRTL(par_);
-	int const endlabel = getEndLabel(pit_, text_);
+	int const endlabel = getEndLabel(row_.pit(), text_);
 
 	// paint imaginary end-of-paragraph character
 
@@ -626,11 +626,11 @@ void RowPainter::paintSelection() const
 		return;
 	Cursor const & curs = pi_.base.bv->cursor();
 	DocIterator beg = curs.selectionBegin();
-	beg.pit() = pit_;
+	beg.pit() = row_.pit();
 	beg.pos() = row_.sel_beg;
 
 	DocIterator end = curs.selectionEnd();
-	end.pit() = pit_;
+	end.pit() = row_.pit();
 	end.pos() = row_.sel_end;
 
 	bool const begin_boundary = beg.pos() >= row_.endpos();
diff --git a/src/RowPainter.h b/src/RowPainter.h
index 5ad1662ac6..05ab57c51b 100644
--- a/src/RowPainter.h
+++ b/src/RowPainter.h
@@ -43,7 +43,7 @@ class RowPainter {
 public:
 	/// initialise and run painter
 	RowPainter(PainterInfo & pi, Text const & text,
-		pit_type pit, Row const & row, int x, int y);
+	           Row const & row, int x, int y);
 
 	/// paint various parts
 	/// FIXME: transfer to TextMetrics
@@ -86,7 +86,6 @@ private:
 	Row const & row_;
 
 	/// Row's paragraph
-	pit_type const pit_;
 	Paragraph const & par_;
 	ParagraphMetrics const & pm_;
 
diff --git a/src/TextMetrics.cpp b/src/TextMetrics.cpp
index a1f3892a8c..c10348d0d8 100644
--- a/src/TextMetrics.cpp
+++ b/src/TextMetrics.cpp
@@ -445,8 +445,9 @@ bool TextMetrics::redoParagraph(pit_type const pit)
 		Row & row = pm.rows()[row_index];
 		row.pit(pit);
 		row.pos(first);
-		need_new_row = breakRow(row, right_margin, pit);
-		setRowHeight(row, pit);
+		row.pit(pit);
+		need_new_row = breakRow(row, right_margin);
+		setRowHeight(row);
 		row.setChanged(false);
 		if (row_index || row.endpos() < par.size()
 		    || (row.right_boundary() && par.inInset().lyxCode() != CELL_CODE)) {
@@ -463,7 +464,7 @@ bool TextMetrics::redoParagraph(pit_type const pit)
 				dim_.wid = max_width_;
 		}
 		int const max_row_width = max(dim_.wid, row.width());
-		computeRowMetrics(pit, row, max_row_width);
+		computeRowMetrics(row, max_row_width);
 		first = row.endpos();
 		++row_index;
 
@@ -563,13 +564,12 @@ LyXAlignment TextMetrics::getAlign(Paragraph const & par, Row const & row) const
 }
 
 
-void TextMetrics::computeRowMetrics(pit_type const pit,
-		Row & row, int width) const
+void TextMetrics::computeRowMetrics(Row & row, int width) const
 {
 	row.label_hfill = 0;
 	row.separator = 0;
 
-	Paragraph const & par = text_->getPar(pit);
+	Paragraph const & par = text_->getPar(row.pit());
 
 	int const w = width - row.right_margin - row.width();
 	// FIXME: put back this assertion when the crash on new doc is solved.
@@ -593,11 +593,11 @@ void TextMetrics::computeRowMetrics(pit_type const pit,
 			++nlh;
 
 		if (nlh && !par.getLabelWidthString().empty())
-			row.label_hfill = labelFill(pit, row) / double(nlh);
+			row.label_hfill = labelFill(row) / double(nlh);
 	}
 
 	// are there any hfills in the row?
-	ParagraphMetrics & pm = par_metrics_[pit];
+	ParagraphMetrics & pm = par_metrics_[row.pit()];
 	int nh = numberOfHfills(row, pm, par.beginOfBody());
 	int hfill = 0;
 	int hfill_rem = 0;
@@ -674,9 +674,9 @@ void TextMetrics::computeRowMetrics(pit_type const pit,
 }
 
 
-int TextMetrics::labelFill(pit_type const pit, Row const & row) const
+int TextMetrics::labelFill(Row const & row) const
 {
-	Paragraph const & par = text_->getPar(pit);
+	Paragraph const & par = text_->getPar(row.pit());
 	LBUFERR(par.beginOfBody() > 0 || par.isEnvSeparator(0));
 
 	int w = 0;
@@ -787,9 +787,9 @@ private:
  * very sensitive to small changes :) Note that part of the
  * intelligence is also in Row::shortenIfNeeded.
  */
-bool TextMetrics::breakRow(Row & row, int const right_margin, pit_type const pit) const
+bool TextMetrics::breakRow(Row & row, int const right_margin) const
 {
-	Paragraph const & par = text_->getPar(pit);
+	Paragraph const & par = text_->getPar(row.pit());
 	pos_type const end = par.size();
 	pos_type const pos = row.pos();
 	pos_type const body_pos = par.beginOfBody();
@@ -797,7 +797,7 @@ bool TextMetrics::breakRow(Row & row, int const right_margin, pit_type const pit
 	bool need_new_row = false;
 
 	row.clear();
-	row.left_margin = leftMargin(max_width_, pit, pos);
+	row.left_margin = leftMargin(max_width_, row.pit(), pos);
 	row.right_margin = right_margin;
 	if (is_rtl)
 		swap(row.left_margin, row.right_margin);
@@ -823,13 +823,13 @@ bool TextMetrics::breakRow(Row & row, int const right_margin, pit_type const pit
 	// check for possible inline completion
 	DocIterator const & ic_it = bv_->inlineCompletionPos();
 	pos_type ic_pos = -1;
-	if (ic_it.inTexted() && ic_it.text() == text_ && ic_it.pit() == pit)
+	if (ic_it.inTexted() && ic_it.text() == text_ && ic_it.pit() == row.pit())
 		ic_pos = ic_it.pos();
 
 	// Now we iterate through until we reach the right margin
 	// or the end of the par, then build a representation of the row.
 	pos_type i = pos;
-	FontIterator fi = FontIterator(*this, par, pit, pos);
+	FontIterator fi = FontIterator(*this, par, row.pit(), pos);
 	do {
 		// this can happen for an empty row after a newline
 		if (i >= end)
@@ -849,7 +849,7 @@ bool TextMetrics::breakRow(Row & row, int const right_margin, pit_type const pit
 			// this is needed to make sure that the row width is correct
 			row.finalizeLast();
 			int const add = max(fm.width(par.layout().labelsep),
-					    labelEnd(pit) - row.width());
+			                    labelEnd(row.pit()) - row.width());
 			row.addSpace(i, add, *fi, par.lookupChange(i));
 		} else if (c == '\t')
 			row.addSpace(i, theFontMetrics(*fi).width(from_ascii("    ")),
@@ -906,11 +906,11 @@ bool TextMetrics::breakRow(Row & row, int const right_margin, pit_type const pit
 	// End of paragraph marker
 	ParagraphList const & pars = text_->paragraphs();
 	if (lyxrc.paragraph_markers && !need_new_row
-	    && i == end && size_type(pit + 1) < pars.size()) {
+	    && i == end && size_type(row.pit() + 1) < pars.size()) {
 		// add a virtual element for the end-of-paragraph
 		// marker; it is shown on screen, but does not exist
 		// in the paragraph.
-		Font f(text_->layoutFont(pit));
+		Font f(text_->layoutFont(row.pit()));
 		f.fontInfo().setColor(Color_paragraphmarker);
 		BufferParams const & bparams
 			= text_->inset().buffer().params();
@@ -931,16 +931,15 @@ bool TextMetrics::breakRow(Row & row, int const right_margin, pit_type const pit
 }
 
 
-void TextMetrics::setRowHeight(Row & row, pit_type const pit,
-				    bool topBottomSpace) const
+void TextMetrics::setRowHeight(Row & row, bool topBottomSpace) const
 {
-	Paragraph const & par = text_->getPar(pit);
+	Paragraph const & par = text_->getPar(row.pit());
 	Layout const & layout = par.layout();
 	double const spacing_val = layout.spacing.getValue()
 		* text_->spacing(par);
 
 	// Initial value for ascent (useful if row is empty).
-	Font const font = displayFont(pit, row.pos());
+	Font const font = displayFont(row.pit(), row.pos());
 	FontMetrics const & fm = theFontMetrics(font);
 	int maxasc = int(fm.maxAscent() * spacing_val);
 	int maxdes = int(fm.maxDescent() * spacing_val);
@@ -978,10 +977,10 @@ void TextMetrics::setRowHeight(Row & row, pit_type const pit,
 		if (bufparams.paragraph_separation == BufferParams::ParagraphSkipSeparation
 		    && !inset.getLayout().parbreakIsNewline()
 		    && !par.layout().parbreak_is_newline
-		    && pit > 0
+		    && row.pit() > 0
 		    && ((layout.isParagraph() && par.getDepth() == 0)
-			    || (pars[pit - 1].layout().isParagraph()
-				    && pars[pit - 1].getDepth() == 0))) {
+			    || (pars[row.pit() - 1].layout().isParagraph()
+				    && pars[row.pit() - 1].getDepth() == 0))) {
 			maxasc += bufparams.getDefSkip().inPixels(*bv_);
 		}
 
@@ -990,7 +989,7 @@ void TextMetrics::setRowHeight(Row & row, pit_type const pit,
 
 		// special code for the top label
 		if (layout.labelIsAbove()
-		    && (!layout.isParagraphGroup() || text_->isFirstInSequence(pit))
+		    && (!layout.isParagraphGroup() || text_->isFirstInSequence(row.pit()))
 		    && !par.labelString().empty()) {
 			FontInfo labelfont = text_->labelFont(par);
 			FontMetrics const & lfm = theFontMetrics(labelfont);
@@ -1005,24 +1004,24 @@ void TextMetrics::setRowHeight(Row & row, pit_type const pit,
 		// a section, or between the items of a itemize or enumerate
 		// environment.
 
-		pit_type prev = text_->depthHook(pit, par.getDepth());
+		pit_type prev = text_->depthHook(row.pit(), par.getDepth());
 		Paragraph const & prevpar = pars[prev];
-		if (prev != pit
+		if (prev != row.pit()
 		    && prevpar.layout() == layout
 		    && prevpar.getDepth() == par.getDepth()
 		    && prevpar.getLabelWidthString()
 					== par.getLabelWidthString()) {
 			layoutasc = layout.itemsep * dh;
-		} else if (pit != 0 || row.pos() != 0) {
+		} else if (row.pit() != 0 || row.pos() != 0) {
 			if (layout.topsep > 0)
 				layoutasc = layout.topsep * dh;
 		}
 
-		prev = text_->outerHook(pit);
+		prev = text_->outerHook(row.pit());
 		if (prev != pit_type(pars.size())) {
 			maxasc += int(pars[prev].layout().parsep * dh);
-		} else if (pit != 0) {
-			Paragraph const & prevpar = pars[pit - 1];
+		} else if (row.pit() != 0) {
+			Paragraph const & prevpar = pars[row.pit() - 1];
 			if (prevpar.getDepth() != 0 ||
 					prevpar.layout() == layout) {
 				maxasc += int(layout.parsep * dh);
@@ -1035,9 +1034,9 @@ void TextMetrics::setRowHeight(Row & row, pit_type const pit,
 		// add the layout spaces, for example before and after
 		// a section, or between the items of a itemize or enumerate
 		// environment
-		pit_type nextpit = pit + 1;
+		pit_type nextpit = row.pit() + 1;
 		if (nextpit != pit_type(pars.size())) {
-			pit_type cpit = pit;
+			pit_type cpit = row.pit();
 
 			if (pars[cpit].getDepth() > pars[nextpit].getDepth()) {
 				double usual = pars[cpit].layout().bottomsep * dh;
@@ -1056,8 +1055,8 @@ void TextMetrics::setRowHeight(Row & row, pit_type const pit,
 	}
 
 	// incalculate the layout spaces
-	maxasc += int(layoutasc  * 2 / (2 + pars[pit].getDepth()));
-	maxdes += int(layoutdesc * 2 / (2 + pars[pit].getDepth()));
+	maxasc += int(layoutasc  * 2 / (2 + pars[row.pit()].getDepth()));
+	maxdes += int(layoutdesc * 2 / (2 + pars[row.pit()].getDepth()));
 
 	row.dimension().asc = maxasc + labeladdon;
 	row.dimension().des = maxdes;
@@ -1593,17 +1592,17 @@ void TextMetrics::deleteLineForward(Cursor & cur)
 }
 
 
-bool TextMetrics::isLastRow(pit_type pit, Row const & row) const
+bool TextMetrics::isLastRow(Row const & row) const
 {
 	ParagraphList const & pars = text_->paragraphs();
-	return row.endpos() >= pars[pit].size()
-		&& pit + 1 == pit_type(pars.size());
+	return row.endpos() >= pars[row.pit()].size()
+		&& row.pit() + 1 == pit_type(pars.size());
 }
 
 
-bool TextMetrics::isFirstRow(pit_type pit, Row const & row) const
+bool TextMetrics::isFirstRow(Row const & row) const
 {
-	return row.pos() == 0 && pit == 0;
+	return row.pos() == 0 && row.pit() == 0;
 }
 
 
@@ -1843,7 +1842,7 @@ void TextMetrics::drawParagraph(PainterInfo & pi, pit_type const pit, int const
 			if (i)
 				y += row.ascent();
 
-			RowPainter rp(pi, *text_, pit, row, row_x, y);
+			RowPainter rp(pi, *text_, row, row_x, y);
 
 			rp.paintOnlyInsets();
 			y += row.descent();
@@ -1887,7 +1886,7 @@ void TextMetrics::drawParagraph(PainterInfo & pi, pit_type const pit, int const
 		if (i)
 			y += row.ascent();
 
-		RowPainter rp(pi, *text_, pit, row, row_x, y);
+		RowPainter rp(pi, *text_, row, row_x, y);
 
 		// It is not needed to draw on screen if we are not inside.
 		bool const inside = (y + row.descent() >= 0
@@ -2012,7 +2011,7 @@ void TextMetrics::completionPosAndDim(Cursor const & cur, int & x, int & y,
 	Row row;
 	row.pos(wordStart.pos());
 	row.endpos(bvcur.pos());
-	setRowHeight(row, bvcur.pit(), false);
+	setRowHeight(row, false);
 	dim = row.dimension();
 	dim.wid = abs(rxy.x_ - lxy.x_);
 
diff --git a/src/TextMetrics.h b/src/TextMetrics.h
index 8d2a12c4e9..069c38a2ac 100644
--- a/src/TextMetrics.h
+++ b/src/TextMetrics.h
@@ -116,15 +116,14 @@ public:
 	/// Returns the height of the row (width member is set to 0).
 	/// If \c topBottomSpace is true, extra space is added for the
 	/// top and bottom row.
-	void setRowHeight(Row & row, pit_type const pit,
-			  bool topBottomSpace = true) const;
+	void setRowHeight(Row & row, bool topBottomSpace = true) const;
 
 private:
 	///
 	ParagraphMetrics & parMetrics(pit_type, bool redo_paragraph);
 
 	/// the minimum space a manual label needs on the screen in pixels
-	int labelFill(pit_type const pit, Row const & row) const;
+	int labelFill(Row const & row) const;
 
 	/// FIXME??
 	int labelEnd(pit_type const pit) const;
@@ -132,13 +131,13 @@ private:
 	/// sets row.end to the pos value *after* which a row should break.
 	/// for example, the pos after which isNewLine(pos) == true
 	/// \return true when another row is required (after a newline)
-	bool breakRow(Row & row, int right_margin, pit_type const pit) const;
+	bool breakRow(Row & row, int right_margin) const;
 
 	// Expand the alignment of row \param row in paragraph \param par
 	LyXAlignment getAlign(Paragraph const & par, Row const & row) const;
 	/** this calculates the specified parameters. needed when setting
 	 * the cursor and when creating a visible row */
-	void computeRowMetrics(pit_type pit, Row & row, int width) const;
+	void computeRowMetrics(Row & row, int width) const;
 
 	// Helper function for the other checkInsetHit method.
 	InsetList::InsetTable * checkInsetHit(pit_type pit, int x, int y);
@@ -208,9 +207,9 @@ public:
 	void deleteLineForward(Cursor & cur);
 
 	/// is this row the last in the text?
-	bool isLastRow(pit_type pit, Row const & row) const;
+	bool isLastRow(Row const & row) const;
 	/// is this row the first in the text?
-	bool isFirstRow(pit_type pit, Row const & row) const;
+	bool isFirstRow(Row const & row) const;
 
 	/// Returns an inset if inset was hit, or 0 if not.
 	/// \warning This method is not recursive! It will return the