diff --git a/libraries/ast/fitstable.c b/libraries/ast/fitstable.c
index b920bd71a27..172a0bececa 100644
--- a/libraries/ast/fitstable.c
+++ b/libraries/ast/fitstable.c
@@ -944,6 +944,9 @@ static void GenerateColumns( AstFitsTable *this, AstFitsChan *header,
 /* Check the global error status. */
    if ( !astOK ) return;
 
+/* Initialise */
+   type = AST__BADTYPE;
+
 /* Get the number of columns defined in the header. */
    if( !astGetFitsI( header, "TFIELDS", &ncol ) ) ncol = 0;
 
@@ -991,7 +994,6 @@ static void GenerateColumns( AstFitsTable *this, AstFitsChan *header,
          type = AST__STRINGTYPE;
 
       } else if( astOK ){
-         type = AST__BADTYPE;
          astError( AST__BDFTS, "astFitsTable: Keyword '%s' in supplied FITS "
                    "binary table header has unsupported value '%s'.", status,
                    keyword, cval );
@@ -1243,6 +1245,9 @@ f     AST_COLUMNNULL functiom.
 /* Check the global error status. */
    if ( !astOK ) return;
 
+/* Initialise */
+   nb = 0;
+
 /* Find the number of bytes needed to hold a single element of the value
    in a column cell. */
    type = astGetColumnType( this, column );
@@ -1265,7 +1270,6 @@ f     AST_COLUMNNULL functiom.
       nb = sizeof( char );
 
    } else if( astOK ) {
-      nb = 0;
       astError( AST__INTER, "astGetColumnData(%s): Unsupported column type "
                 "%d (internal AST programming error).", status,
                 astGetClass( this ), type );
@@ -1951,6 +1955,9 @@ f        The global status.
 /* Check the global error status. */
    if ( !astOK ) return;
 
+/* Initialise */
+   nb = 0;
+
 /* Find the number of bytes in the supplied array holding a single element
    of the value in a column cell. */
    type = astGetColumnType( this, column );
@@ -1973,7 +1980,6 @@ f        The global status.
       nb = sizeof( char );
 
    } else if( astOK ) {
-      nb = 0;
       astError( AST__INTER, "astPutColumnData(%s): Unsupported column type "
                 "%d (internal AST programming error).", status,
                 astGetClass( this ), type );
diff --git a/libraries/ast/mapping.c b/libraries/ast/mapping.c
index 1297de3c920..e629789aac3 100644
--- a/libraries/ast/mapping.c
+++ b/libraries/ast/mapping.c
@@ -1200,6 +1200,8 @@ static double FindGradient( AstMapping *map, double *at, int ax1, int ax2,
    interval. */
    y1 = AST__BAD;
    y2 = AST__BAD;
+   gmax = AST__BAD;
+   gmin = AST__BAD;
    ngood = 0;
 
    for( i = 0; i < RATE_ORDER; i++ ) {
@@ -1209,7 +1211,7 @@ static double FindGradient( AstMapping *map, double *at, int ax1, int ax2,
 
          g = ( y[ i + 1 ] - y[ i ] )/( x[ i + 1 ] - x[ i ] );
 
-         if( i == 0 ) {
+         if( ngood == 1 ) {
             gmax = gmin = g;
          } else if( g < gmin ) {
             gmin = g;
@@ -7833,6 +7835,11 @@ static double MatrixDet( int nrow, int ncol, const double *matrix, int *status )
 /* Check the global error status. */
    if ( !astOK ) return result;
 
+/* Initialise... */
+   sqmat = NULL;
+   nrowuse = 0;
+   ncoluse = 0;
+
 /* Flag any rows and columns that should be ignored because they contain
    only bad values or zeros. */
    userow = astCalloc( nrow, sizeof( *userow ) );
@@ -7849,12 +7856,10 @@ static double MatrixDet( int nrow, int ncol, const double *matrix, int *status )
       }
 
 /* Find the number of usable rows and columns. */
-      nrowuse = 0;
       for( irow = 0; irow < nrow; irow++ ) {
          if( userow[ irow ] ) nrowuse++;
       }
 
-      ncoluse = 0;
       for( icol = 0; icol < ncol; icol++ ) {
          if( usecol[ icol ] ) ncoluse++;
       }