diff --git a/compile.go b/compile.go
index 69f98d4..bb58baf 100644
--- a/compile.go
+++ b/compile.go
@@ -16,7 +16,9 @@ type section struct {
 }
 
 type symtabEntry struct {
-	symtabSectionIndex int
+	// The index of this symbol within the whole symtab
+	symtabSectionIndex  int
+	name_shstrtabOffset int
 
 	sectionName string
 	kind        string
@@ -41,55 +43,79 @@ func NewCompiler() *compiler {
 	// First, there's an all-zero entry that is reserved for extended ELF headers
 	c.sections = append(c.sections, section{})
 
+	// Real entry: shstrtab
 	c.sections = append(c.sections, section{
-		name:                `.shstrtab`, // Mandatory: the table that names sections themselves
-		name_shstrtabOffset: 1,
-		buff:                &bytes.Buffer{},
+		name: `.shstrtab`, // Mandatory: the table that names sections themselves
+		buff: &bytes.Buffer{},
 	})
 	c.shstrtab = &c.sections[1]
+
 	// The first byte in a string table is conventionally expected be \x00, so that you can reference
 	// null strings with it
-	c.shstrtab.buff.WriteByte(0)
+	c.StringTable("")
 
-	c.shstrtab.buff.WriteString(c.shstrtab.name)
-	c.shstrtab.buff.WriteByte(0)
+	c.shstrtab.name_shstrtabOffset = c.StringTable(c.shstrtab.name)
 
 	return c
 }
 
+func (c *compiler) StringTable(text string) int {
+	pos := c.shstrtab.buff.Len()
+
+	c.shstrtab.buff.WriteString(text)
+	c.shstrtab.buff.WriteByte(0)
+
+	return pos
+}
+
 func (c *compiler) CreateSymbol(name string, class string, offset int64, length int64, global bool) error {
 
 	if _, ok := c.symtab[name]; ok {
 		return fmt.Errorf("Symbol %q already exists", name)
 	}
 
+	// fmt.Printf("--> CreateSymbol(%s)\n", name)
+
 	// Find the .symtab section, or create if it does not exist
 	symtabSec := c.FindOrCreateSection(`.symtab`)
+	if symtabSec.buff.Len() == 0 {
+		// First time initialized
+
+		// Add a zeroth symtab entry - zero is a sentinel, not a usable entry
+		symtabSec.buff.Write(make([]byte, 8*3))
+	}
 
 	// New entry index = length / len(entry) = length / 24
 	nextIndex := symtabSec.buff.Len() / 24
 
 	// Add to our fast lookup table
-	c.symtab[name] = symtabEntry{
+	ste := symtabEntry{
 		symtabSectionIndex: nextIndex,
-
-		sectionName: c.currentSection.name,
-		kind:        class,
-		offset:      offset,
-		global:      global,
-		length:      length,
+		kind:               class,
+		offset:             offset,
+		global:             global,
+		length:             length,
 	}
 
 	// Find the section index for the section containing this symbol
-	sectionIndex := -1
-	for i, _ := range c.sections {
-		if c.sections[i].name == c.currentSection.name {
-			sectionIndex = i
-			break
+	var srcSectionIdx int = 0
+	var sttType uint8 = STT_NOTYPE
+
+	if class == `.section` {
+		ste.sectionName = name
+		srcSectionIdx = len(c.sections) - 1 // The most recent added section
+		sttType = STT_SECTION
+
+	} else if c.currentSection != nil {
+		ste.sectionName = c.currentSection.name
+		var ok bool
+		srcSectionIdx, ok = c.FindSectionIndex(c.currentSection.name)
+		if !ok {
+			panic("current section does not exist?")
 		}
-	}
-	if sectionIndex == -1 {
-		return fmt.Errorf("Current section missing index")
+
+	} else {
+		panic("Symbol is neither a section, nor within a section (?)")
 	}
 
 	// Add to the .symtab section
@@ -97,14 +123,42 @@ func (c *compiler) CreateSymbol(name string, class string, offset int64, length
 	// created, linking it with any other .o files will create a combined .text
 	// section where all the offsets have shifted
 	esym := Elf64_Sym{}
-	esym.st_name = 0 // Default: unnamed
-	esym.st_info = STT_SECTION | (STB_LOCAL << 4)
-	esym.st_other = STV_HIDDEN // For this translation unit only
-	esym.st_shndx = uint16(sectionIndex)
+
+	if class == `.section` {
+		esym.st_name = uint32(c.StringTable(name)) // Write name into public string table
+		esym.st_info = sttType | (STB_LOCAL << 4)
+		esym.st_other = STV_DEFAULT
+		esym.st_shndx = uint16(srcSectionIdx)
+
+	} else if global {
+		esym.st_name = uint32(c.StringTable(name)) // Write name into public string table
+		esym.st_info = sttType | (STB_GLOBAL << 4)
+		esym.st_other = STV_DEFAULT
+		esym.st_shndx = uint16(srcSectionIdx)
+
+	} else {
+		// Private variable for this translation unit
+		// Needs an entry, but no need to expose the name
+		esym.st_name = 0 // uint32(c.StringTable(name)) // Write name into public string table // 0 // Default: unnamed (0th entry in our string table is \x00)
+		esym.st_info = sttType | (STB_LOCAL << 4)
+		esym.st_other = STV_HIDDEN // For this translation unit only
+		esym.st_shndx = uint16(srcSectionIdx)
+	}
+
+	fmt.Printf("-->New symbol %q in section %q (sectionidx %v)\n", name, ste.sectionName, srcSectionIdx)
+
 	esym.st_size = uint64(length)
 
 	err := binary.Write(symtabSec.buff, binary.LittleEndian, &esym)
-	return err
+	if err != nil {
+		return err
+	}
+
+	// Stash in symtabEntry
+	ste.name_shstrtabOffset = int(esym.st_name)
+	c.symtab[name] = ste
+
+	return nil
 }
 
 func (c *compiler) Must(b []byte) {
@@ -149,18 +203,24 @@ func (c *compiler) FindOrCreateSection(sectionName string) *section {
 
 	// No section with this name. Create it
 	c.sections = append(c.sections, section{
-		name:                sectionName,
-		name_shstrtabOffset: c.shstrtab.buff.Len(),
-		buff:                &bytes.Buffer{},
+		name: sectionName,
+		buff: &bytes.Buffer{},
 	})
+	sec := &c.sections[len(c.sections)-1]
 
-	c.shstrtab.buff.WriteString(sectionName)
-	c.shstrtab.buff.WriteByte(0)
+	// Create a symbol for it
+	// This creates a string table entry for us
+	err := c.CreateSymbol(sectionName, ".section", 0, 0, true)
+	if err != nil {
+		panic("CreateSymbol: " + err.Error())
+	}
 
-	return &c.sections[len(c.sections)-1]
+	sec.name_shstrtabOffset = c.StringTable(sectionName)
+
+	return sec
 }
 
-func (c *compiler) Reloc(symbolName string, mode ElfRelocationType, addOffset int64) error {
+func (c *compiler) Reloc(symbolName string, mode ElfRelocationType) error {
 	// Find '.rela.{currentsection}', creating it if it does not exist
 	var relaSec *section = c.FindOrCreateSection(`.rela` + c.currentSection.name)
 
@@ -170,11 +230,19 @@ func (c *compiler) Reloc(symbolName string, mode ElfRelocationType, addOffset in
 		return fmt.Errorf("Reference to unknown symbol %q", symbolName)
 	}
 
+	// Find the symbol pointing to its parent section
+	parentSectionSyminfo, ok := c.symtab[syminfo.sectionName]
+	if !ok {
+		return fmt.Errorf("Bad parent section")
+	}
+
+	fmt.Printf("-->Relocation %q found in %q (sectionidx %d)\n", symbolName, syminfo.sectionName, parentSectionSyminfo.symtabSectionIndex)
+
 	// Add the relocation to the .rela section
 	rr := Elf64_Rela{}
 	rr.r_offset = uint64(c.currentSection.buff.Len())
-	rr.r_info = uint64(syminfo.symtabSectionIndex)<<32 | uint64(mode) // high bits: Index of search symbol in the symtab. low bits: mode type
-	rr.r_addend = addOffset
+	rr.r_info = uint64(parentSectionSyminfo.symtabSectionIndex)<<32 | uint64(mode) // high bits: Index of search symbol in the symtab (the source section). low bits: mode type
+	rr.r_addend = syminfo.offset                                                   // Add to the result when relocating (offset within source section)
 
 	err := binary.Write(relaSec.buff, binary.LittleEndian, &rr)
 	if err != nil {
@@ -235,7 +303,7 @@ func (c *compiler) Compile(t Token) error {
 			return fmt.Errorf("variable %q has unknown size class %q", tok.VarName, tok.Sizeclass)
 		}
 
-		err := c.CreateSymbol(tok.VarName, ".var."+tok.Sizeclass, int64(c.currentSection.buff.Len()), position-int64(c.currentSection.buff.Len()), false)
+		err := c.CreateSymbol(tok.VarName, ".var."+tok.Sizeclass, int64(position), int64(c.currentSection.buff.Len())-position, false)
 		if err != nil {
 			return err
 		}
@@ -293,7 +361,7 @@ func (c *compiler) Compile(t Token) error {
 				panic("mov $var,rax pattern: missing case")
 			}
 
-			err = c.Reloc(tok.Args[0][1:], R_X86_64_32S, 0) // Declare that this is a 32-bit reloc, not a 64-bit one
+			err = c.Reloc(tok.Args[0][1:], R_X86_64_32S) // Declare that this is a 32-bit reloc, not a 64-bit one
 			if err != nil {
 				return fmt.Errorf("mov with relocation: %w", err)
 			}
@@ -313,7 +381,7 @@ func (c *compiler) Compile(t Token) error {
 				panic("mov rxx,$var pattern: missing case")
 			}
 
-			err = c.Reloc(tok.Args[1][1:], R_X86_64_32S, 0) // Declare that this is a 32-bit reloc, not a 64-bit one
+			err = c.Reloc(tok.Args[1][1:], R_X86_64_32S) // Declare that this is a 32-bit reloc, not a 64-bit one
 			if err != nil {
 				return fmt.Errorf("mov with relocation: %w", err)
 			}
@@ -339,7 +407,7 @@ func (c *compiler) Compile(t Token) error {
 				panic("mov $var,rxx pattern: missing case")
 			}
 
-			err = c.Reloc(tok.Args[1][2:], R_X86_64_64, 0)
+			err = c.Reloc(tok.Args[1][2:], R_X86_64_64)
 			if err != nil {
 				return fmt.Errorf("mov with relocation: %w", err)
 			}
@@ -428,33 +496,38 @@ func (c *compiler) Finalize(dest io.Writer) error {
 		shdr := Elf64_Shdr{}
 
 		shdr.sh_name = uint32(sec.name_shstrtabOffset)
-
-		// Default (unknown section):
-		// Treat as extra read-only data (.rodata)
-		shdr.sh_type = 1     // SHT_PROGBITS, program data
-		shdr.sh_flags = 0x10 // MERGE
+		shdr.sh_addralign = 1 // Not doing any proper alignment
 
 		switch sec.name {
 		case ".text":
 			shdr.sh_type = SHT_PROGBITS
-			shdr.sh_flags = 0x2 | 0x4 | 0x10 // WRITE|ALLOC|MERGE
+			shdr.sh_flags = SHF_ALLOC | SHF_EXECINSTR
+
 		case ".data":
 			shdr.sh_type = SHT_PROGBITS
-			shdr.sh_flags = 0x2 | 0x10 // WRITE|MERGE
+			shdr.sh_flags = SHF_WRITE | SHF_ALLOC
+
 		case ".symtab":
 			shdr.sh_type = SHT_SYMTAB
-			shdr.sh_flags = 0x10 | 0x20 // MERGE|STRINGS
-			shdr.sh_info = uint32(len(c.symtab))
-			shdr.sh_entsize = uint64(sec.buff.Len()) // Number of fixed-sized symtab entries
-			shdr.sh_link = 1                         // The index of the section containing the actual strings. We reuse shstrtab(!?!)
+			shdr.sh_flags = 0
+			shdr.sh_info = uint32(len(c.symtab) + 1)
+			shdr.sh_entsize = 24 // Size in bytes of each entry
+			shdr.sh_link = 1     // The index of the section containing the actual strings. We reuse shstrtab(!?!)
+
 		case ".shstrtab":
 			shdr.sh_type = SHT_STRTAB
-			shdr.sh_flags = 0x10 | 0x20 // MERGE|STRINGS
+			shdr.sh_flags = 0
+
+		case ".rodata":
+			shdr.sh_type = SHT_PROGBITS
+			shdr.sh_flags = SHF_ALLOC
+
 		default:
 			if strings.HasPrefix(sec.name, ".rela.") {
 				shdr.sh_type = SHT_RELA
-				shdr.sh_flags = 0                         // ?
-				shdr.sh_link = uint32(symtabSectionIndex) // The index of the symtab section
+				shdr.sh_flags = 0 // ?
+				shdr.sh_link = uint32(symtabSectionIndex)
+				shdr.sh_entsize = 24 // Size in bytes of each entry
 
 				// Find the index of the section for which this relocates. Match by name
 				srcSectionIdx, ok := c.FindSectionIndex(sec.name[5:])
@@ -462,6 +535,8 @@ func (c *compiler) Finalize(dest io.Writer) error {
 					return fmt.Errorf("Missing parent section for relocation section %q", sec.name)
 				}
 				shdr.sh_info = uint32(srcSectionIdx)
+			} else {
+				return fmt.Errorf("don't know the right flags to use for section %q", sec.name)
 			}
 		}
 
diff --git a/elf.go b/elf.go
index 9f34653..dbefd9f 100644
--- a/elf.go
+++ b/elf.go
@@ -57,6 +57,17 @@ const (
 	SHT_PREINIT_ARRAY = 16
 	SHT_GROUP         = 17
 	SHT_SYMTAB_SHNDX  = 18
+
+	SHF_WRITE            = 0x1
+	SHF_ALLOC            = 0x2
+	SHF_EXECINSTR        = 0x4
+	SHF_MERGE            = 0x10
+	SHF_STRINGS          = 0x20
+	SHF_INFO_LINK        = 0x40
+	SHF_LINK_ORDER       = 0x80
+	SHF_OS_NONCONFORMING = 0x100
+	SHF_GROUP            = 0x200
+	SHF_TLS              = 0x400
 )
 
 // Elf64_Shdr is the Section header