From the Pentium Processor User's Manual, Volume 1: Pentium Processor Data Book, section 3.1.2.

The Pentium processor can issue one or two instructions every clock. In order to issue two instructions simultaneously they must satisfy the following conditions:

• Both instructions in the pair must be "simple" as defined below
• There must be no read-after-write or write-after-write register dependencies between them
• Neither instruction may contain both a displacement and an immediate
• Instructions with prefixes (other than 0F of JCC instructions) can only occur in the u-pipe Simple instructions are entirely hardwired; they do not require any microcode control and, in general, execute in one clock. The exceptions are the ALU mem,reg and ALU reg,mem instructions which are two and three clock operations respectively. Sequencing hardware is used to allow them to function as simple instructions. The following integer instructions are considered simple and may be paired:
  
  1. mov reg, reg/mem/imm
  2. mov mem, reg/imm
  3. alu reg, reg/mem/imm
  4. alu mem, reg/imm
  5. inc reg/mem
  6. dec reg/mem
  7. push reg/mem
  8. pop reg
  9. lea reg, mem
  10. jmp/call/jcc near
  11. nop
  In addition, conditional and unconditional branches may be paired only if they occur as the second instruction in the pair. They may not be paired with the next sequential instruction. Also, SHIFT/ROT by 1 and SHIFT by imm may pair as the first instruction in a pair.
  
  The register dependencies that prohibit instruction pairing include implicit dependencies via registers or flags not explicitly encoded in the instruction. For example, an ALU instruction in the u-pipe (which sets the flags) may not be paired with an ADC or a SBB instruction in the v-pipe. There are two exceptions to this rule. The first is the commonly occurring sequence of compare and branch which may be paired. The second exception is pairs of pushes or pops. Although these instructions have an implicit dependency on the stack pointer, special hardware is included to allow these common operations to proceed in parallel.
  
  Although in general two paired instructions may proceed in parallel independently, there is an exception for paired "read-modify-write" instructions. Read-modify-write instructions are ALU operations with an operand in memory. When two of these instructions are paired there is a sequencing delay of two clocks in addition to the three clocks required to execute the individual instructions.
  
  Although instructions may execute in parallel their behavior as seen by the programmer is exactly the same as if they were executed sequentially (as on the Intel486(TM) CPU).